Former Talks since SS 05
[SS05][WS05/06][SS06][WS06/07][SS07][HS07][HS08][SS09]
SS 09
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05.03.2009
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Paul Doukhan (University of Cergy-Pontoise, France)
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Long range and short range dependence of times series: modelling and applications
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract: The talk aims at exhibiting some properties of times series; following
ideas of Herold Dehling we better distinguish dependence properties
through their asymptotic distribution, more closely related with
statistical fitting (eg. through tests and confidence intervals). Long
and short range dependences are considered and various examples of
models with those properties are exhibited. For short range dependences
we introduce a weak dependence frame (Doukhan and Louhichi, 1999) which
provides wide ranges of models and mainly avoids the problems occurring
with previously defined weak dependences. We consider general,
nonlinear, nonGaussian, nonMarkov models with specific properties useful
for applications (integer valued, memory models etc...).
Finally we list applications for both classes of dependences to show
what use may be done of those notions and models.
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12.03.2009
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Alexandre Roch (Cornell University, Ithaca, USA)
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Liquidity Risk, Price Impacts and the Replication Problem
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract: We extend the model of liquidity risk of Cetin et al. (2004) to allow
for price impacts. Starting from simple principles, we show that the impact of a
trade on prices is directly proportional to the size of the transaction and the amount
of liquidity of the asset. This leads to a new characterization of
self-financing trading strategies and a sufficient condition for no arbitrage. We
show that, with the
use of volatility swaps, contingent claims whose payoffs depend on the
value of the asset can be approximately replicated. The replicating
costs of such payoffs are obtained from the solutions of BSDEs with quadratic growth and
analytical properties of
these solutions are investigated.
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19.03.2009
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Keita Owari (Hitotsubashi University, Japan)
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Robust Exponential Hedging and Indifference Valuation
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 16.15 - 17.15
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Abstract: abstract.pdf
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19.03.2009
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Jiro Akahori (Ritsumeikan University, Japan)
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Thermodynamic Approach to Equilibrium in Insurance Markets (joint work with M. Nishida and Y. Seto)
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract: To attack the classical puzzle of
adverse selection in insurance market,
we introduce a multi-agent model
where the state of each agent (insured)
is described by a Markov process. By taking a bulk limit, a macroscopic
model is obtained.
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25.03.2009
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Peter Carr (New York University, New York, USA)
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What does an option price mean?
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 11.00 - 12.00
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Abstract:
It is well known that the market price of a standard option reflects
the risk-neutral mean of its path-independent payoff. It is less well
known that this same option price also reflects the risk-neutral mean
of various path-dependent payoffs. We give several examples of such
payoffs which together suggest that option prices convey much more
information than one might initially expect.
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Slides: slides.pdf
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26.03.2009
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Pavel Gapeev (London School of Economics)
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Valuation of American options in models with two risky assets and stochastic interest rates
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
We study the problems of rational valuation of perpetual American
options in two diffusion models of financial markets. The initial
problems are embedded into the associated optimal stopping problems for
necessarily two-dimensional continuous Markov processes. The latter
problems are reduced to their equivalent parabolic-type free-boundary
problems. Applying a change-of-variable formula with local time on
surfaces, we prove that the unique solutions of the free-boundary
problems provide solutions of the initial optimal stopping problems.
In
the first model, the short-term interest rate is a constant and the
market prices of two risky assets (e.g. currencies) are modelled by two
exponential diffusion processes driven by constantly correlated
Brownian motions. We consider valuation of American options whose
payoffs are convex functions of both asset prices at the time of
exercise. Imposing certain additional regularity conditions on the
option payoffs, we show that optimal exercise boundaries for one asset
price are convex or concave functions of the current price of another
asset. Based on the analysis of the appropriate free-boundary
problems, we provide a characterization of options whose rational
values admit explicit expressions. Such contracts have the payoff
structure similar to one of Margrabe (or exchangeable) power options,
which are used for reducing exchange risk in currency markets. Using
the resulting closed form solutions, we determine asymptotic behaviour
for value functions of more complicated American spread and basket
options on two underlying assets.
In the second
model, the interest rate dynamics is modelled by a mean-reverting
affine diffusion process (Vasicek's model) with reflection at zero, and
the market price of one risky asset is described by a geometric
diffusion process. Both processes are driven by constantly correlated
Brownian motions. We consider valuation of American standard (call and
put) options on the underlying asset. We show that optimal exercise
boundaries for the asset price are convex or concave functions of the
current interest rate values. Since the initial standard option
problems do not admit closed form solutions, we introduce specially
modified options with strikes depending on the interest rate value at
the time of exercise. Based on the analysis of the appropriate
free-boundary problems, we provide a characterization of strike
functions of the constructed options whose rational values admit
explicit expressions. Using the resulting closed form solutions, we
determine asymptotic behaviour for value functions of the initial
American standard options with constant strikes.
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02.04.2009
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Konstantinos Fokianos (University of Cyprus)
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Linear and log-linear Poisson autoregression
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
The talk considers geometric ergodicity and likelihood-based inference
for linear and loglinear Poisson autoregressions. In the linear case,
the conditional
mean is linked linearly to its past values as well as the observed
values
of the Poisson process. This also applies to the conditional variance,
implying an interpretation as an integer valued GARCH process. In a
loglinear conditional Poisson model,
the conditional mean is a loglinear function of its past values and a
nonlinear function of past observations. Under geometric ergodicity,
the maximum likelihood estimators
of the parameters are shown to be asymptotically Gaussian in the linear
model. In addition we provide a consistent
estimator of the asymptotic covariance, which is used in the
simulations and the analysis of some transaction data. Our approach to
verifying geometric ergodicity proceeds via Markov theory and
irreducibility. Finding transparent conditions for proving ergodicity
turns out to be a delicate problem in the original model formulation.
This
problem is circumvented by allowing a perturbation of the model. We
show that as the perturbations can be chosen to be arbitrarily small,
the differences between the perturbed and non-perturbed versions vanish
as far as the asymptotic distribution of the parameter estimates is
concerned.
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16.04.2009
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No seminar (Easter)
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23.04.2009
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Peter Haas (IBM Almaden Research Center, San Jose, CA, USA)
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On recurrence and transience in heavy-tailed generalized semi-Markov processes
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
The generalized semi-Markov process (GSMP) is the usual model for the
underlying stochastic process of a complex discrete-event system. It
is important to understand fundamental behavioral properties of the
GSMP model, such as the conditions under which the states of a GSMP are
recurrent. For example, the recurrence or non-recurrence of a
specified "single state" determines whether or not the successive exit
times from the state can be used as a sequence of regeneration points
for purposes of steady-state simulation output analysis. We review
some sufficient conditions for recurrence in irreducible finite-state
GSMPs; these conditions include requirements on the "clocks" that
govern the occurrence of state transitions. For example, each
clock-setting distribution must have finite mean. We then show that,
in contrast to ordinary semi-Markov processes, an irreducible
finite-state GSMP can have transient states in the presence of multiple
clock-setting distributions with heavy tails.
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30.04.2009
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Catalin Starica (Université de Neuchâtel)
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The stock markets of Europe: Globalization or European Integration?
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract: abstract.pdf
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14.05.2009
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Hansjörg Albrecher (Université de Lausanne)
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On refracted stochastic processes and the analysis of insurance risk
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
We show a somewhat surprising identity for first passage probabilities
of spectrally-negative Levy processes that are refracted at their
running maximum and discuss extensions of this identity and its
application in the study of insurance risk processes in the presence of
tax payments. In addition, we discuss a statistic that is related to
the sample coefficient of variation which leads to an alternative
simple method for estimating the extreme value index of Pareto-type
tails from corresponding iid claim data with infinite variance.
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22.05.2009
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Ludger Rüschendorf (University of Freiburg, Germany)
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On risk measures for portfolio vectors and a related diversification problem
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ETHZ, HG G19.2, 14.15 - 15.15
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Abstract:
After an introduction to risk measures for portfolio vectors the main
part of this talk is concerned with the discussion of the influence of
stochastic dependence on various risk functionals. In particular we
discuss and review developments on the distributional transform, on
Frechet type bounds with univariate and multivariate marginals, and on
various dependence orderings. In the final part we apply these ordering
results to aggregation risk measures and to the diversification
problem. In the framework of multivariate extreme value theory we
determine risk optimal portfolios and consider statistical properties
of the empirical versions.
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22.05.2009
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Giovanni Puccetti (University of Firenze, Italy)
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The AEP algorithm for the fast computation of the distribution of the sum of dependent random variables
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ETHZ, HG G19.2, 15.15 - 16.15
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Abstract: We propose a new algorithm to compute numerically the distribution
function of the sum of d dependent, non-negative random variables with
a given joint distribution. (Joint work with P. Arbenz and P. Embrechts.)
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28.05.2009
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Sidney Resnick (Cornell University)
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The conditional extreme value model
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 18.15 - 19.15
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Abstract:
The conditional extreme value (CEV) model is an alternative to
multivariate extreme value modeling and is potentially applicable to
modeling the distribution of a random vector if either some component
of the vector is not in a unidimensional domain of attraction or else
asymptotic independence requires supplementary lower order
information. We survey properties and characterizations of this model,
mention how it is related to standard and classical theory and outline
detection techniques. Current applications include applying the
methodology to data network sessions segmented by percentiles of a peak
rate variable. (Joint work at various times with Jan Heffernan,
Bikramjit Das, Luis Lopez-Oliveros.)
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HS 08
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25.09.2008
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Catherine Donnelly (ETH, Zurich)
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Convex duality in constrained mean-variance portfolio optimization under a regime-switching model
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
We solve a mean-variance portfolio optimization problem with portfolio
constraints under a regime-switching model. Specifically, we seek a
portfolio process which minimizes the variance of the terminal wealth,
subject to a terminal wealth constraint and convex portfolio
constraints. The regime-switching is modeled using a finite state
space, continuous-time Markov chain and the market parameters are
allowed to be random processes.
We establish the existence and
characterization of the solution to the given problem using a convex
duality method. The solution is characterized in terms of the market
parameters, the filtration and the solution to the dual problem.
We
also present a martingale representation theorem for processes which
are locally square-integrable martingales with respect to the
filtration generated by a Brownian motion and a finite state space,
continuous-time Markov chain.
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02.10.2008
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Raphael Hauser (Oxford University)
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Structured Uncertainty Sets in Robust Portfolio Optimization
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
Decision tools in risk management figure amongst the oldest
applications of numerical optimization. Optimization models that arise
in this context typically rely on model parameters. In practical
applications these parameters have to be estimated and are therefore
not known with certainty. To mitigate the effects of instability of
optimal investment decisions as a function of the model parameters,
robust optimization aims at finding solutions that behave well for all
points in an uncertainty set for the model parameters. The existing
literature thereby largely treats uncertainty in parameters that model
risk independently of parameters that model expected returns. We argue
that - in the typical situation where return data cannot be
independently sampled but is available through historical data -
functional dependencies between the risk and expected return terms of
the model parameters arise naturally, leading to structured uncertainty
sets that are smaller and less pessimistic than the standard models
considered in the literature. We show that several new portfolio
optimization models based on structured uncertainty sets that reside in
quadratic manifolds have equivalent reformulations as convex quadratic
programming problems. Our numerical results based on real market data
suggest that the practical performance of our new models compares
favorably with existing methods. Coauthor: Denis Zuev, Oxford Centre
for Industrial and Applied Mathematics
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07.10.2008
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Mark Podolskij (ETH, Zurich)
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Limit theorems for functionals of semimartingales plus noise
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract: First of all, we provide a review of the recent limit theorems for
functionals of (noiseless) semimartingales.
Then we present some limit theorems for certain functionals
of moving averages of semimartingales plus noise, which are observed at
high frequency. Our method
generalizes the pre-averaging approach originally proposed by Podolskij
and Vetter (2006)
and provides consistent estimates for various characteristics of general
semimartingales. Furthermore, we prove the associated (stable) central
limit theorems. The corresponding convergence rate is n-1/4, which
is known to be optimal
in the parametric case.
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21.10.2008
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Mico Loretan (Bank for International Settlements, Hong Kong)
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Frequency of observation and the estimation of integrated volatility in deep and liquid financial markets
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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23.10.2008
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Elyes Jouini (Dauphine University, Paris)
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Strategic beliefs
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 16.15 - 17.15
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Abstract:
We provide a discipline for beliefs formation through a model of
subjective beliefs, in which agents hold incorrect but strategic
beliefs. More precisely, we consider beliefs as a strategic variable
that agents can manipulate to maximize their utility from trade. Our
framework is therefore an imperfect competition framework, and the
underlying concept is the concept of Nash equilibrium. We find that a
strategic behavior leads to beliefs subjectivity and heterogeneity.
Optimism (resp. overconfidence) as well as pessimism (resp. doubt) both
emerge as optimal beliefs. Furthermore, we obtain a positive
correlation between pessimism (resp. doubt) and risk-tolerance. The
consensus belief is pessimistic and, as a consequence, the risk premium
is higher than in a standard setting. Our model is embedded in a
standard financial markets equilibrium problem and may be applied to
several other situations in which agents have to choose the optimal
exposure to a risk (choice of an optimal retention rate for an
insurance company, choice of the optimal proportion of equity to retain
for an entrepreneur and for a given project).
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30.10.2008
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No seminar: FINRISK site visit by the SNSF Review Panel
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6.11.2008
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Location:
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ETHZ, HG G19.2
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13.30
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Peter Friz (University of Cambridge)
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On the Black-Scholes volatility
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Abstract:
We consider risk-neutral returns and show how their tail asymptotics
translate directly to large strike asymptotics of the Black-Scholes
implied volatility smile. The theory of regular variation is the ideal
mathematical framework to formulate and prove our results.
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16.00
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Damir Filipovic (Vienna Institute of Finance)
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Collateralized Debt Obligations – a top-down framework
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Abstract:
Collateralized Debt Obligations (CDOs) have gained much attention
during the recent financial market crisis. CDO is an encompassing term
that stands for securities backed by a pool of reference entities such
as bonds, loans, or credit default swaps. Modeling CDOs has become a
vital topic in the last years both for academics and practitioners.
In
this talk, I briefly discuss the building blocks (insuring, pooling and
tranching credit risk) of CDOs and their role in the current financial
crisis. The main topic is a unifying top-down framework for valuing
contingent claims on a CDO, which I have recently developed in a joint
paper with Thorsten Schmidt and Ludger Overbeck (“Dynamic CDO Term
Structure Modeling”). Top-down means that we focus on the normalized
aggregate loss process in the underlying pool. A defaultable (T,x)-bond
is defined as a security which pays one if the loss process has not
exceeded the level x at maturity T, and zero else. (T,x)-bonds turn out
to be the fundamental basis components for the hedging and pricing of
any CDO derivative. (T,x)-bonds can be factorized into their default
and market (“forward spread”) risk components. This representation
corresponds to a stylized fact of financial markets: spread risk is
what primarily drives CDO values; the objective default risk is
secondary. The forward spread surface movements are exogenously
specified, taking account of contagion effects from the loss process.
Necessary and sufficient conditions for the absence of arbitrage lead
to a non-classical stochastic differential equation for the forward
spreads. Under technical conditions, it can be shown that any
exogenously specified spread volatility and contagion parameters induce
a unique (in law) consistent loss process and thus an arbitrage-free
family of (T,x)-bond prices. For computational efficiency, analytically
tractable doubly stochastic affine term structure models are at hand. I
will conclude with an outlook on some related open problems.
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7.11.2008
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Location:
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ETHZ, HG G19.2
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08.15
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Mete Soner (Sabanci University Istanbul)
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Stochastic optimal control in finance
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Abstract::
Since the classical paper of Merton on the optimal consumption and
investment problem, stochastic optimal control has been widely used in
financial and economic modeling. These applications also fundamentally
shaped the development of the theory of optimal control. Indeed,
recently introduced control problem classes, such as singular optimal
control or stochastic target, are all motivated by financial
applications. On the solution side there have been two parallel
approaches. For Markovian problems, dynamic programming and partial
differential equations provide a computationally tractable technique.
This solution was well developed over the past decades. A rich
activity was also seen for non-Markovian models. The main tools here
have been convex duality and modern probability theory.
In this
talk, chiefly we will give a brief survey of these developments,
outline the techniques and their connections, and also discuss several
recent applications to finance. These applications are in markets with
constraints and in models for liquidity.
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10.30
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Josef Teichmann (Vienna University of Technology)
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A new approach to stochastic partial differential equations with applications to mathematical finance
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Abstract:
Inspired by questions from mathematical finance we develop a new
approach to stochastic partial differential equations, which allows to
derive (high-order) numerical schemes and the respective convergence
rates for weak and strong approximations. Those schemes are applied to
pricing and simulation problems in mathematical finance, for instance
in risk management. We show results on a scenario generator, which is
calibrated to the market and evaluated by one of the presented schemes.
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14.15
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Alexander Schied (Cornell University, Ithaca)
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Optimal portfolio liquidation in illiquid markets
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Abstract:
A variety of circumstances can force a market participant to liquidate
an asset position that is so large that selling it will significantly
impact the underlying asset price. In this talk, we will discuss the
problem of constructing optimized liquidation algorithms. This problem
is interesting from several points of view. First, it has a high
practical significance. Second, it allows studying the economics of
liquidity risk in their purest form. Third, the nonlinear feedback
effects of trading large orders lead to some interesting and
challenging mathematical problems.
Depending on the choice of the
model, we can get results for a simple criterion such as the
minimization of the expected costs or for the more difficult task of
maximizing the expected utility of the seller. In the latter case, the
optimal strategy is characterized by fully nonlinear PDEs. Sensitivity
analysis for solutions of these PDEs yields qualitative properties of
the strategy depending on the absolute risk aversion of the utility
function. If time permits, we also comment on the particularly
interesting situation when competing traders become aware of the
seller's intention and try to make a profit out of it. This talk is
based on joint papers with Aurélien Alfonsi, Antje Fruth, and Torsten
Schöneborn.
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13.11.2008
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Sergei Levendorskii (University of Leicester)
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Refined and enhanced FFT techniques, with applications to pricing barrier options and their sensitivities
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract: Many mathematical methods of option pricing rely on one's
ability to calculate the action of certain integro-differential
operators and convolution operators quickly and efficiently. In turn,
the latter computations are based on FFT techniques. However, in many
important cases, a straightforward application of FFT and iFFT leads to
errors of several kind, which cannot be made simultaneously small
(uncertainty principle) unless grids with too many points are used. We
develop an approach to using FFT techniques that gives one more
flexibility in controlling the aforementioned errors, and, at the same
time, yields fast and efficient algorithms. As applications, using
Carr's randomization, we compute the prices and sensitivities of
barrier options and first-touch digital options on stocks whose
log-price follows a L\'evy process. The numerical results obtained via
our approach are demonstrated to be in good agreement with the results
obtained using other (sometimes fundamentally different) approaches
that exist in the literature. However, our method is computationally
much faster (often, dozens of times faster). Moreover, our technique
has the advantage that its application does not entail a detailed
analysis of the underlying L\'evy process: one only needs an explicit
analytic formula for the characteristic exponent of the process. Thus
our algorithm is very easy to implement in practice. Finally, our
method yields accurate results for a wide range of values of the spot
price, including those that are very close to the barrier, regardless
of whether the maturity period of the option is long or short. A
natural extension of the method gives similar results for
double-barrier options. (Mitya Boyarchenko and Sergei Levendorskii)
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19.11.2008
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Kerry Back (Texas A&M University )
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Open Loop Equilibria and Perfect Competition in Option Exercise Games
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ETHZ, HG G19.1, 17.15 - 18.15
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Abstract: The investment boundaries defined by Grenadier (2002) for an
oligopoly investment game determine equilibria in open loop
strategies. As closed loop strategies, they are not equilibria,
because any firm by investing sooner can preempt the investments of
other firms and expropriate the growth options. The perfectly
competitive outcome is produced by closed loop strategies that are
mutually best responses. In this equilibrium, the option to delay
investment has zero value, and the simple NPV rule is followed by all
firms.
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27.11.2008
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David Hobson (University of Warwick)
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Recovering models consistent with perpetual put prices.
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
The standard paradigm in mathematical finance is to postulate a model
and to use this model to derive option prices. However, there is a
growing literature on the inverse problem; given a set of option
prices, can we recover a model which is consistent with those prices?
For example, given all European vanilla option prices we can recover a
unique martingale diffusion consistent with those prices.
Alternatively, given all European put prices at a single maturity we
can recover from solutions of the Skorokhod embedding problem a model
which is consistent with observed prices and which leads to the largest
possible price for an exotic derivative.
In this talk, based on
joint work with Erik Ekstrom, we consider the problem of finding a
time-homogeneous process which is consistent with
perpetual American put prices.
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04.12.2008
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Mathias Vetter (Ruhr-University Bochum, Germany)
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Testing the parametric form of volatility in diffusion models corrupted by noise
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
Assume that one has a latent price process given by a continuous Ito
semimartingale, which can be observed in a high-frequency setting
(thus: the process lives on a fixed time interval [0,1] and the
observation times are i/n for growing n). In this case, Dette and
Podolskij (2008) have provided a test for a given parametric hypothesis
on the volatility function at the rate n^{-1/2}. However, empirical
research suggests that the underlying semimartingale is rather latent
than observed, and thus one assumes that the observations are
contaminated by additive noise. This talk deals with the solution for
testing for a specific form of volatility in this different framework.
We obtain results which have similar features to the ones in Dette and
Podolskij, but converge at worse rates, which are depending on the
actual structure of the hypothesis.
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11.12.2008
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Luciano Campi (Dauphine University, Paris)
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Multivariate Utility Maximization with Proportional Transaction Costs
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
We present an optimal investment theorem for a currency exchange model
with random proportional transaction costs. The investor's preferences
are represented by a smooth, multivariate utility function, allowing
for simultaneous consumption of any prescribed selection of the
currencies at a given terminal date. We prove the existence of an
optimal portfolio process under the assumption of asymptotic
satiability of the value function. Sufficient conditions for asymptotic
satiability of the value function include reasonable asymptotic
elasticity of the utility function, or a growth condition on its dual
function. We show that the portfolio optimization problem can be
reformulated in terms of maximization of a terminal liquidation utility
function, and that both problems have a common optimizer.
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18.12.2008
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Bikramjit Das (Cornell University, Ithaca)
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Conditional extreme value limit models: characterization and detection techniques
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
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Abstract:
Multivariate extreme value theory assumes a multivariate domain of
attraction condition for the distribution of a random vector
necessitating that each component satisfy a marginal domain of
attraction condition. Heffernan & Tawn (2004) and Heffernan &
Resnick (2007) developed an approximation to the joint distribution of
the random vector by conditioning on one of the components being in an
extreme-value domain. The usual method of analysis using multivariate
extreme value theory often is not helpful either because of asymptotic
independence or due to one component of the observation vector not
being in a domain of attraction which we can overcome by using the
conditional model. The prior papers left unresolved the consistency of
different models obtained by conditioning on different components being
extreme and we provide understanding of this issue. We also clarify the
relationship between the conditional distributions and multivariate
extreme value theory and extensions from one to the other. We also
discuss the relationship between the conditional extreme value model
and standard regular variation on cones of the form
$[0,\infty]x(0,\infty]$ or $(0,\infty]x [0,\infty]$. An important
characterization of this model is in terms of the limit measure forming
a product or not which leads to a dichotomy in estimation of the model
parameters. We propose three statistics which act as tools to detect
the plausibility of using this model as well as whether it is a product
or not.
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HS 07
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04.10.2007
|
Tahir Choulli (University of Alberta, Canada)
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Comparing two optimal martingale measures
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
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|
Abstract:
In this talk, I will present a comparative study between the minimal
Hellinger martingale measure of order q (MHM(q) measure hereafter) and
the q-optimal martingale measure, for any q and any semimartingale
market model. I will explain how these two optimal martingale measures
are obtained, and then I will discuss their characterizations.The
comparison between these two martingale measures is conducted in two
ways.The first comparison deals with comparing `physically' the two
optimal martingale measures. Precisely, in this case, I will show that
the two optimal martingale measures coincide for any Levy market
model with known horizon, while they differ in general. I will also
provide necessary and sufficient conditions for the two optimal
martingale measures to coincide in a general framework. The second
comparison addresses the question whether there exists a model for
which the MHM(q) measure of the underlying model is the q-optimal
martingale measure, and vice-versa. This last comparison is intimately
related to uncertainty models. Finally, I will analyze the MHM(q)
measure for the case of discrete-time market model. This talk is based
on a joint work with Christophe Stricker.
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11.10.2007
|
Shianjian Tang (Fudan University, China)
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Investment under Uncertainty, and Related Multi-Dimensional BSDEs with Oblique Reflection
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract:
Since Dixit's well-known paper "Entry and Exit Decisions Under
Uncertainty" (Journal of Political Economy, 620-638, 1989), there is a
renewed interest in application of optimal stochastic switching in
economic and financial modeling and analysis. In this talk, I would
address my recent work (jointed with Ying Hu ) on the optimal switching
of BSDEs, and the related multi-dimensional BSDEs with oblique
reflection. Some further extensions will also be given.
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15.10.2007
|
Walter Schachermayer (Universität Wien)
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In which Financial Markets does the Mutual Fund Theorem hold true?
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ETHZ, HG G19.1, 17.15 - 18.15
|
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Abstract: article pdf
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18.10.2007
|
Peter Bank (TU Berlin)
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A large investor model with market indifference prices
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract:
We study the wealth dynamics of a large investor who dynamically trades
with a number of market makers. At any point, the market makers fill
his order at a price that is determined by the unique Pareto optimal
allocation which accomodates the investor's desired position and which
leaves the market makers' utilities unchanged. We show how the dynamics
of such market indifference prices can be described by an SDE for the
market makers' utilities and discuss some implications for pricing and
hedging in illiquid financial markets.
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25.10.2007
|
Takuji Arai (Keito University, Tokio)
|
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Generalizations of mean-variance hedging
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract:
Two generalizations of mean-variance hedging will be introduced in this
talk. The first is the L^p-hedging, and another is optimal hedging
problem based on a symmetric function. The L^p-hedging is an extension
of the mean-variance hedging problem to the L^p-setting, where 1<p.
Remark that the mean-variance hedging is corresponding to the case
where p=2. A representation of the optimal hedging strategy in the
L^p-sense is obtained as the L^p-projection of the underlying
contingent claim onto a suitable space of stochastic integrations.
Moreover, the valuation problem induced by the L^p-projections
naturally is discussed. In the second par of this talk, we consider an
optimal hedging which minimizes the expectation of an asymmetric
function of the difference between the underlying contingent claim and
the value of portfolio at the maturity. In particular, under some
assumptions, we shall prove the unique existence of a solution and
shall discuss its mathematical property.
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01.11.2007
|
Monique Jeanblanc (Université Evry)
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Dynamical Modelling of Successive Defaults
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract:
In this paper, we present a new approach to dynamically model the
dependence between default times, based on the knowledge of the
conditional survival probability. We first show that this framework
provides a systematic method to obtain computation of conditional
expectations. We then extend the framework to several default times,
particularly for successive defaults.
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08.11.2007
|
Larbi Alili (Warwick University)
|
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On some functional transformations related to the time-inversion property and applications to some first passage problems
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract:
We review the time transformations allowing to construct Brownian
bridges from a Brownian motion. These are generalized to semi-stable
or self-similar Markov process enjoying the time inversion property. We
present some related functional transformations and study their
properties. In the boudary crossing context, the latter family
naturally maps the space of continuous real-valued functions into a
another space of functions. We establish a simple and explicit formula
relating the distributions of the first hitting times of each of these
by a self-similar Markov process enjoying the time-inversion property.
|
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15.11.2007
|
Darrell Duffie (Stanford University)
|
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Information Percolation
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract:
We study information percolation is a stylized over-the-counter market
in which a large set of asymmetrically informed investors meet in small
groups over time, exchanging information with their counterparties when
matched, through their bids for an asset. We provide an explicit
solution for the dynamic evolution of the cross-sectional distribution
of posterior beliefs regarding the asset payoff. We calculate the rate
of convergence of the cross-sectional distribution of beliefs to a
common posterior. We show that this convergence rate does not depend on
the size of the
groups of investors that meet. The convergence rate
is merely the mean aggregate meeting rate of the investor population.
Some open problems are discussed. (Paper co-written with Gaston Giroux, and Gustavo Manso).
|
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22.11.2007
|
Ulrich Horst (University of British Columbia, Canada)
|
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Risk Minimization and Optimal Derivative Design in a Principal Agent Game
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract:
We consider the problem of Adverse Selection and optimal derivative
design within a Principal-Agent framework. The principal's income is
exposed to non-hedgeable risk factors arising, for instance, from
weather or climate phenomena. She evaluates her risk using a coherent
and law invariant risk measure and tries minimize her exposure by
selling derivative securities on her income to individual agents. The
agents have mean-variance preferences with heterogeneous risk aversion
coefficients. An agent's degree of risk aversion is private information
and hidden to the principal who only knows the overall distribution. We
show that the principal's risk minimization
problem
has a solution and illustrate the effects of risk transfer on her
income by means of two specific examples. Our model extends earlier
work of Barrieu and El Karoui (2005) and Carlier, Ekeland and Touzi
(2007). The talk is based on joint work with Santiago Moreno.
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29.11.2007
|
1. Evelyn Buckwar (Humboldt-Universität zu Berlin)
|
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Numerical treatment of stochastic delay differential equations
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 16.15 - 17.15
|
|
|
Abstract:
In this talk I will first present an introduction to stochastic delay
differential equations and provide some application examples. Further,
I will highlight some issues in their numerical treatment and present
some recent results, which are based on joint work with R. Kuske, S.
Mohammed and T. Shardlow.
|
|
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2. Ioannis Karatzas (Columbia University)
|
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Volatility stabilization, diversity and arbitrage in stochastic finance
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract: In this talk we start with an overview of the modern theory of portfolios,
based on Stochastic Analysis. We introduce the notion of relative arbitrage
and provide simple, easy-to-test criteria for the existence of such
arbitrage in equity markets. These criteria postulate essentially that the
excess growth rate of the market portfolio, a positive quantity that can be
estimated or even computed from a given market structure, be "sufficiently
large". We show that conditions which satisfy these criteria are manifestly
present in the US equity market, and construct explicit portfolios under
these conditions. One such condition, market diversity, emerges when the
volatility structure is bounded.
We then construct examples of abstract markets in which the criteria hold.
We study in some detail a specific example of a non-diverse abstract market
which is volatility-stabilized, in that the return from the market portfolio
has constant drift and variance rates, while the smallest stocks are
assigned the largest volatilities and individual stocks fluctuate widely. An
interesting probabilistic structure emerges in which time changes, Bessel
processes, and the asymptotic theory for planar Brownian motion, play
crucial roles. Several open questions are raised for further study. (Joint
work with E. Robert Fernholz.)
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06.12.2007
|
Jerome Reboulleau (Ecole Polytechnique Federale, Lausanne)
|
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|
The Shipping Derivatives Market and the Levy Market Model
|
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|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract:
Historically, freight rates are more volatile than other,commodities.
Prices for shipping contracts often vary by more than 60% in the course
of a single year and the various actors in this industry are demanding
new tools in order to hedge their risk. As a response to this demand,
shipping derivatives have been successfully introduced in 2001, leading
to a market of 50bn USD in 2006 (source HSBC Shipping Services). Due to
this large volatility, only models with jumps, such as Lévy processes,
are realistic. For example, the work by Bakshi & Madan (2000)
provides a basis to price such derivatives either by way of Maximum
Likelihood (MLE) or Minimum Mean Square Error (MMSE) directly using the
characteristic function. After an introduction to the shipping market,
a real-time application of this technology will be presented such as
vessel revenue valuation and shipping derivatives trading strategies.
|
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13.12.2007
|
Mike Tehranchi (Cambridge University)
|
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|
Static and dynamic no-arbitrage option prices
|
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|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
|
|
Abstract:
In recent years, there has been growing interest in an HJM-style
approach to the joint modelling of equity and derivative prices. In
this talk, the complicated interaction of the static and dynamic
no-arbitrage condition is explored in the context of a model for
European call options.
|
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20.12.2007
|
Patrick Cheridito (Princeton University)
|
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|
Risk measures on Orlicz hearts
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
SS 07
|
28.03.2007
|
ETH HG E 41
|
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09.15 - 10.15: Semen Mark Malamud: "A unified approach to market incompleteness"
|
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10.35 - 11.35: Rafael Schmidt: "Modelling Dynamic Portfolio Risk using risk drivers of elliptical processes"
|
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11.35 - 12.35: Michael Kupper: "Equilibrium Pricing in Incomplete Markets"
|
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29.03.2007
|
Ying Hu (Université Rennes 1)
|
|
|
Ergodic Backward Stochastic Differential Equation and Ergodic Control
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract: see pdf-file
|
|
12.04.2007
|
Colloquium 90th birthday Prof. Dr. Eckman
|
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26.04.2007
|
Freddy Delbaen (ETH Zürich)
|
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|
Backward Stochastic Differential Equations and Monetary Utility Functions
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
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3.05.2007
|
Ilya Molchanov (Universität Bern)
|
|
|
Convex geometry, stability and extreme values
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract.
The talk explains a number of relationships between multivariate stable
and multivariate extreme values distributions and concepts related to
convex geometry and random sets. In particular, it is shown that
multivariate extreme value distributions with standardised Frechet
marginals correspond to norms generated by convex sets that appear as
expectations of a random cross-polytopes. In the classical case of
stable distributions with the characteristic exponent 1, the convex
sets that characterise the dependency structure are known in geometry
under the name of zonoids, while for other stable distributions some
generalisations of zonoids are discussed.
|
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10.05.2007
|
Michael Taksar (University of Missouri, Columbia, USA)/
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Some new results and open problems in diffusion optimization
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract.
In the modern insurance business, the issue of reinsurance as well as
investment of the surplus are one of the major financial decision the
company must make. While reinsurance reduces risk, it also diverts
part of the premium stream to the reinsurance company. Likewise less
risky investments in the stock market yield a smaller potential profit.
Balancing the risk with potential profit looms large whenever such
decisions are made. We will consider a model of an insurance companies
with different modes of risk and financial control. Different types of
reinsurance correspond to the risk reduction techniques of the
insurance, while financial control corresponds to a more familiar
portfolio rebalancing. There are different objective which the company
may pursue. One is the classical minimization of the ruin
probabilities. Another one is the dividend pay-out
maximization.
The later merges with the classical finance issue of utility
optimization by a small investor, pioneered by Merton. It is possible
to obtain a closed form solution to many problems and see the structure
of the optimal policy. Mathematically, the problem reduces to to a
solution of nonlinear ordinary or partial differential equations which
in more complicated cases can be done numerically. We will present
recent results as well as open problems.
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24.05.2007
|
Huyen Pham (Université Paris 7)
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Impulse control on finite horizon with execution delay
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract:
We consider impulse control problems in finite horizon for diffusions
with decision lag and execution delay. The new feature is that our
general framework deals with the important case when several
consecutive orders may be decided before the effective execution of the
first one. This is motivated by financial applications in the trading
of illiquid assets such as hedge funds. We show that the value
functions for such control problems satisfy a suitable version of
dynamic programming principle in finite dimension, which takes into
account the past dependence of state process through the pending
orders. The corresponding Bellman partial differential equations (PDE)
system is derived, and exhibit some peculiarities on the coupled
equations, domains and boundary conditions. We prove a unique
characterization of the value functions to this nonstandard PDE system
by means of viscosity solutions. We then provide an algorithm to find
the value functions and the optimal control. This easily implementable
algorithm involves backward and forward iterations on the domains and
the value functions, which appear in turn as original arguments in the
proofs for the boundary conditions and uniqueness results. Some
numerical experiments illustrate the impact of execution delay on
financial decision making. (joint work with Benjamin Bruder).
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31.05.2007
|
Pauline Barrieu (London School of Economics)
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On Pareto-optimal allocations for multi-period risks (joint with Giacomo Scandolo).
|
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.00 - 18.15
|
|
|
Abstract.
In this paper, we consider the problem of Pareto optimal allocation in
a general framework, involving preference functionals defined on a
general real vector space. The optimization problem is equivalent to a
modified sup-convolution of the different agents' preference
functionals. The results are then applied to a multi-period setting and
some further characterization of Pareto optimality for an allocation is
obtained for expected utility for processes.
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07.06.2007
|
Enzo Giacomini (Humboldt-Universität zu Berlin)
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Inhomogeneous Dependence Modelling with Time Varying Copulae
|
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|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract.
Measuring dependence in a multivariate time series is tantamount to
modelling its dynamic structure in space and time. In the context of a
multivariate normally distributed time series, the evolution of the
covariance (or correlation) matrix over time describes exactly this
dynamic. A wide variety of applications, though, requires a modelling
framework different from the multivariate normal. In risk management
for example, the non-normal behaviour of most financial time series
calls for nonlinear (i.e. non-gaussian) dependency. The correct
modelling of non-gaussian dependencies is therefore a key issue in the
analysis of multivariate time series. In this work we use copulae
functions with adaptively estimated time varying parameters for
modelling the distribution of returns, free from the usual normality
assumptions. Further, we apply copulae to estimation of Value-at-Risk
(VaR) of a portfolio and show its better performance over the
RiskMetrics approach, a widely used methodology for VaR estimation.
|
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14.06.2007
|
Magdalena Kobylanski (Université de Marne-la-Vallée)
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Backward Stochastic Differential Equations with Quadratic Growth and Applications
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract (as pdf-file). We provide existence, comparison and stability results for one-dimensional backward stochastic differential equations (BSDEs)
$$ Y_t= \xi +\int_t^TF(s,Y_s,Z_s)ds -\int-t^T Z_s dW_s \quad 0 \leq t \leq T, $$
when
the cofficient $F$ is continuous and has quadratic growth in $Z$ and
the terminal condition $\xi$ is bounded. We also give, in this
framework, links between the solutions of BSDEs set on a diffusion and
the viscosity or Sobolev solutions of the corresponding semilinear
partial differentail equations. These results apply in particular for
contigent claim pricing via utility maximization.
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21.06.2007
|
Stefan Weber (Cornell University)
|
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|
Optimal Portfolio Choice with Limited Downside Risk
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract.
The measurement and management of the downside risk of portfolios is a
key issue for financial institutions. The industry standard Value at
Risk (VaR) shows serious deficiencies as a measure of the downside
risk. It penalizes diversification in many situations and does not take
into account the size of very large losses exceeding the value at risk.
These problems motivated intense research on alternative static and
dynamic risk measures.
While axiomatic results are an important
first step towards better risk management, an analysis of the economic
implications of different approaches to risk management should not be
neglected. Risk limits influence the behavior of economic agents – and
this impact is not captured by the classical analysis. The talk will
discuss recent research
on portfolio choice under risk constraints.
This includes results of Gundel & Weber, Cuoco, He & Isaenko,
and Pirvu & Zitkovic.
|
WS 06/07
|
01.02.2007
|
Monique Jeanblanc (Evry University, France)
|
|
|
A new tool for pricing defaultable claims: martingale density
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
tba
|
|
25.01.2007
|
Parthanil Roy (Cornell University)
|
|
|
Ergodic Theory, Abelian Groups and Extremes of Stable Random Fields
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. This talk
will focus on the extreme values of stationary symmetric \alpha-stable
random fields over hypercubes of increasing size. We will discuss how
the asymptotic behavior of these extremes can be connected to certain
ergodic theoretical and group theoretical properties of the integral
representation of the random field. This connection helps us to draw
conclusions about long range dependence of such processes. (This is a
joint work with Gennady Samorodnitsky.)
|
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18.01.2007
|
Romuald Elie (Crest, ETH)
|
|
|
Optimal consumption-investment strategy under drawdown constraint
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
We consider the
optimal consumption-investment problem under the drawdown constraint,
i.e. the wealth process never falls below a fixed fraction of its
running maximum. We assume that the risky asset is driven by the
constant coefficients Black and Scholes model and we consider a general
class of utility functions. On an infinite time
horizon, we
provide the value function in explicit form, and we derive closed-form
expressions for the optimal consumption and investment strategy. The
key ingredient for the obtention of the solution relies on the linearity
of
the PDE satisfied by the dual transform of the value function. On a
finite time horizon, we interpret the value function as the unique
viscosity solution of its corresponding Hamilton-Jacobi-Bellman
equation. This leads to a consistent numerical scheme of approximation
and allows for a comparison with the explicit solution in infinite
horizon.
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|
11.01.2007
|
Peter Tankov
|
|
|
Optimal consumption under liquidity risk
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. We
consider a portfolio/consumption choice problem in a market model with
liquidity risk. In this model, the investor can trade and observe stock
prices only at exogenous Poisson arrival times. He may also consume
continuously from his cash holdings, and his goal is to maximize his
expected utility from consumption. This is a mixed discrete/continuous
stochastic control problem, nonstandard in the literature. We show how
the dynamic programming principle leads to a coupled system of
Integro-Differential Equations (IDE), and we prove an analytic
characterization of this control problem by adapting the concept of
viscosity solutions. We also provide a convergent numerical algorithm
for the resolution to this coupled system of IDE, and illustrate our
results with some numerical experiments. (joint work with H. Pham)
|
|
04.01.2007
|
Takahiro Tsuchiya
|
|
|
What is the natural scale for a Lévy process in modelling term structure of interest rates?
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. This
presentation gives examples of explicit arbitrage-free term structure
models with Lévy jumps via state price density approach. By
generalizing quadratic Gaussian models, it is found that the
probability density function of a Lévy process is a "natural" scale for
the process to be the state variable of a market.
|
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21.12.2006
|
Xiaobo Bao
|
|
|
Reflected Backward Stochastic Differential Equations
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
tba
|
|
14.12.2006
|
Marie-Amélie Morlais (IRMAR, Rennes)
|
|
|
Quadratic BSDEs and application to utility maximization problem in two models
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract: TalkSeminar141206.pdf
|
|
07.12.2006
|
Christian Genest (Université Laval, Québec, Canada)
|
|
|
Goodness-of-fit tests for copula models: the state of the art
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. Various
procedures have been proposed recently for goodness-of-fit testing of
copula models. A critical review of these tests will be presented, and
new proposals will be made. A comparative power study will also be
described, based on a Monte Carlo study involving a large number of
copula alternatives and dependence conditions. To circumvent problems
with inaccurate asymptotic approximation of the tests' asymptotic
distributions, these simulations had to rely on a double parametric
bootstrap procedure which will be detailed. Methodological
recommendations will be made. This talk is based on joint work with
David Beaudoin (Université Laval) and Bruno Rémillard (HEC Montréal).
|
|
23.11.2006
|
Celebration Colloquium for Prof. Freddy Delbaen
|
|
|
Please visit the website http://www.math.ethz.ch/~finasto/Delbaen-www/ for more information.
|
|
16.11.2006
|
Jocelyne Bion-Nadal
|
|
|
Dynamic Risk Measures and Bid-Ask Dynamic Pricing
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract: Bion-Nadal-Abstract.pdf
|
|
09.11.2006
|
Sara Biagini (University of Perugia)
|
|
|
On continuity properties and dual representation of convex and monotone functionals on Frechet lattices
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
|
|
02.11.2006
|
Juan Li (Université de Bretagne Occidentale, Brest, France)
|
|
|
Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
|
SS 06
29.06.2006
|
Benoîte de Saporta (INRIA)
|
|
|
Optimal portfolio allocation under transaction costs
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. Consider
a financial market with a bond and a risky asset driven by a geometric
Brownian motion whose return rate changes at random times. The wealth
can be invested either all in the bond ar all in the risky asset, and
each transaction involves a proportional cost. We consider the problem
of maximizing the utility of the terminal wealth. We give both
mathematical and numerical results.
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22.06.2006
|
Andrea Macrina (King's College London)
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Information-Based Asset Pricing
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
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Abstract: MacrinaAbstract20060622.pdf
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22.06.2006
|
Pavel Shevchenko (CSIRO, Australia)
|
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A toy model for operational risk
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 15.30 - 16.30
|
15.06.2006
|
Jörn Sass (Johan Radon Institut, Österreichische Akademie der Wissenschaften)
|
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Maximizing expected utility under convex constraints and partial information
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
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Abstract: SassAbstract20060615.pdf
|
08.06.2006
|
Catalina Stefanescu (London Business School)
|
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Modelling Expected Loss with Unobservable Heterogeneity
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. This
paper develops a framework for modelling and estimating expected loss
over arbitrary horizons in the presence of unobservable heterogeneity.
We jointly model the probability of default and the recovery rate given
default. Unobservable heterogeneity representing the effects of
measurement errors and missing variables, is modelled with a
non-negative latent random variable that acts multiplicatively on the
default intensity function. We estimate the parameters of different
models using a new and extensive default and recovery data set,
containing the majority of defaults of companies listed on the AMEX,
NYSE and NASDAQ between 1980-2004. Our joint model specification
implies that the out-of-sample probability of default and the recovery
rate given default are negatively correlated, and the magnitude of the
correlation varies with the credit cycle.
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01.06.2006
|
Chris Finger (RiskMetrics Group Geneva)
|
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Measuring Risk on Credit Indices: On the Use of the Basis
|
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. In this
paper we examine the evolution of fair spreads on credit indices over
2005 and investigate the various alternatives to provide risk measures
on these products. We first review the mechanics of these indices. We
show how market fair spreads can be decomposed into three components:
the average fair spread over the reference basket, a term representing
the basket heterogeneity, and the basis. From our analysis, this basis
should be understood as an additional risk factor. For a risk manager,
the short lengths of available time series on credit indices is a
challenging problem. Taking into account these three spread components,
we describe a way to create synthetic time series of fair spreads.
These synthetic fair spreads overcome the difficulty and yield
reasonable risk measures.
The paper is available here: FingerPaper20060518.pdf
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22.05.2006
|
Teemu Pennanen (Helsinki School of Economics)
|
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Nonlinear Price Processes
|
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ETHZ, HG E41, 16.30 - 18.00 (Coffee: 16.00 - 16.30)
|
|
|
Abstract.
This paper presents a stochastic model for trading in double
auction markets where the marginal cost of buying is a
nondecreasing function of the number of shares bought.
The model admits a generalized version of the fundamental theorem
of asset pricing.
(Optimization and Applications Seminar)
|
18.05.2006
|
Mario Wüthrich (ETH Zürich)
|
|
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Introduction to the claims reserving problem in non-life insurance
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. Claims
Reserving is one of the central topics in non-life insurance.
Mathematicians and actuaries need to estimate adequate reserves for
open claims. These reserves have a direct influence on all financial
statements, in calculating future premiums and in calculating solvency
margins. In this talk we give an introduction to claims reserving and
we discuss its implications for solvency considerations.
|
11.05.2006
|
Sebastian Maaß (ETH Zürich)
|
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Coherent Capital Allocation for Comonotonic Additive Risk Measures
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract: MaassAbstract20060511.pdf
|
04.05.2006
|
Romuald Elie (CREST / University Paris Dauphine)
|
|
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Discrete time approximation of decoupled Forward-Backward SDE with jumps
|
|
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ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. We study
a discrete-time approximation for solutions of systems of decoupled
forward-backward stochastic differential equations with jumps. Assuming
that the coefficients are Lipschitz-continuous, we prove the
convergence of the scheme when the number of time steps n goes to
infinity.
When the jump coefficient of the first variation process
of the forward component satisfies a non-degeneracy condition which
ensures its inversibility, we obtain the optimal convergence rate
n^(-1/2). The proof is based on a generalization of a remarkable result
on the path-regularity of the solution of the backward equation derived
by Zhang in the no-jump case. A similar result is obtained without the
non-degeneracy assumption whenever the coefficients are C1_b with
Lipschitz derivatives. Several extensions of these results are
discussed. In particular, we propose a convergent scheme for the
resolution of systems of coupled semilinear parabolic PDE's.
|
|
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A preprint of the talk is available on:
http://www.crest.fr/pageperso/elie/Elie_files/Research/BE05.ps
|
27.04.2006
|
John Chadam (University of Pittsburgh)
|
|
|
Free Boundary Problems in Mathematical Finance
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. We
provide a unified approach to studying a wide variety of free boundary
problems that arise in mathematical finance. For the most part, the
main ideas will be presented in the simplest case of the early exercise
boundary for the American put option on a geometric Brownian motion. In
addition to discussing the existence and uniqueness of the solution to
the problem, we will describe several fast and accurate numerical and
analytical approximations for the location of these early exercise
boundaries. Special attention will be paid to the proof and role of the
convexity of the free boundary. The same approach can be used to treat
similar problems with more general underliers such as jump diffusion
processes. We will also mention how the techniques can be carried over
to treat other classes of free boundary problems such as the inverse
first crossing problem of the default barrier of a credit process as
well as the pricing of mortgage prepayment options. Various parts of
this work are joint efforts with Xinfu Chen (Pittsburgh) and David
Saunders (Pittsburgh and Waterloo) as well as a long list of students,
practitioners and foreign collaborators.
|
20.04.2006
|
Dirk Becherer (Imperial College London)
|
|
|
Bounded solutions to Backward SDEs with jumps for utility optimization and indifference hedging
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. We prove
results on bounded solutions to backward stochastic equations driven by
random measures. Those bounded BSDE solutions are then applied to solve
different stochastic optimization problems with exponential utility in
models where the underlying filtration is non-continuous. This includes
results on portfolio optimization under an additional liability and on
dynamic utility indifference valuation and partial hedging in
incomplete financial markets which are exposed to risk from
unpredictable events. In particular, we characterize the limiting
behavior of the utility indifference hedging strategy and of the
indifference value process for vanishing risk aversion.
|
18.04.2006
|
Josef Teichmann (Technische Universität Wien)
|
|
|
Pricing and Hedging by Cubature Methods
|
|
|
ETHZ, HG E33.5, 17.15 - 18.15
|
|
|
Abstract. We
introduce cubature methods on Wiener Space in the spirit of
Kusuoka-Lyons-Victoir. Cubature Methods are well parametrized,
high-order numerical schemes for the quick approximation of prices of
Lischitz Claims. Furthermore the geometry of the analysed SDE-problem
is preserved. On the one hand we can extend these methods to the
calculation of Greeks in Mathematical Finance, on the other hand we are
able to show how the actual calculation of cubature trees can be
quickened by fascinating recombination structures. The applied
mathematical ideas stem from Stochastic Analysis and from the Geometry
of Nilpotent Lie groups. The Bass-Milnor-Wolf result on the number of
lattice points in big balls will be central for the construction of
feasible algorithms. The research was motivated by the (numerical)
analysis of high (or even infinite) dimensional Stochastic Differential
Equations in Mathematical Finance such as Term structure equations.
The
results are mainly contained in Teichmann (Calculation of Greeks by
Cubature Formulas, Proc Royal Soc 2004) and Soreff-Schmeiser-Teichmann
(Recombination of Cubature methods for SDEs, Preprint 2006).
|
07.04.2006
|
Dilip Madan (Robert H. Smith School of Business, University of Maryland)
|
|
|
Equilibrium Asset Pricing with Non-Gaussian
Factors and Exponential Utilities
|
|
|
ETHZ, HG F26.1, 10.30 - 11.30
|
|
|
We analyse the equilibrium asset pricing implications
for an economy with single period return exposures to explicit non-Gaussian,
skewed and potentially long-tailed systematic factors and Gaussian
idiosyncratic components. Investors maximize expected exponential utility and
equilibrium factor prices are shown to reflect exponentially tilted prices for
non-Gaussian factor risk exposures. It is shown that these prices may be
directly estimated from the univariate probability law of the factor exposure,
given an estimate of average risk aversion in the economy. In addition a residual
form of the capital asset pricing model continues to hold and prices the
idiosyncratic or Gaussian risks. The theory is illustrated on data for the US
economy using independent components analysis to identify the factors and the
variance gamma model to describe the probability law of the non-Gaussian
factors. It is shown that the residual CAPM accounts for no more than one
percent of the pricing of risky assets, while the exponentially tilted
systematic factor risk exposures account for the bulk of risky asset pricing.
|
WS 05/06
|
09.02.2006
|
Alexander Schied (TU Berlin)
|
|
|
Some aspects of model uncertainty and robustness in finance
|
|
|
ETHZ, HG E33.5, 16.00 - 17.00!
|
|
|
Abstract. We
present some recent results on the robustness of certain trading
strategies with respect to model uncertainty. In the first part, we
consider the robustness of the Delta hedging stategy of an exotic
derivative with respect to realized volatility, when the underlying
model is a local volatility model. Our analysis is based on volatility
comparison techniques for SDEs. In the second part, we focus on the
construction of optimal investment strategies for an investor who is
averse against both risk and model uncertainty. Here one can use or
combine several techniques including convex duality, nonlinear PDEs,
and robust statistical test theory. In some special cases, the problems
considered in parts one and two are closely related to each other.
|
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02.02.2006
|
Pierre Patie
|
|
|
Explicit law for the first passage time of a Brownian motion over some moving boundaries
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. First
passage time densities of Markov processes over fixed or moving
boundaries are key quantities in many fields of applied mathematics.
For instance, in mathematical finance, it is required for the pricing
of path-dependent or American options. In this talk, we review the
basic properties of a standard Brownian motion (scaling, time
inversion...) and explain how each of them lead to an explicit
expression for the law of the first passage time of the Brownian motion
to some specific curves. Then, we show how to extend these results to
the class of strong Feller Markov processes enjoying one of these
properties.
|
|
26.01.2006
|
Cancelled due to the FINRISK Conference "Risk and Portfolio Management"
|
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19.01.2006
|
Hideatsu Tsukahara (Seijo University)
|
|
|
One-parameter Families of Distortion Risk Measures
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. Based on
Kusuoka's representation theorem for law invariant and comonotonically
additive coherent risk measures, we introduce some parametric families
of distortion risk measures and investigate their properties. And we
compare them with the traditional expected shortfall. Their use and
interpretation in risk management will also be discussed.
|
|
12.01.2006
|
Semyon Malamud and Eugene Trubowitz (ETH Zürich)
|
|
|
Asset pricing in idiosyncratically incomplete markets
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
22.12.2005
|
Patrick Cheridito (Princeton University)
|
|
|
Time-consistency of dynamic utility functions and the decomposition property of acceptance sets
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
15.12.2005
|
Michael Kupper (Princeton University/ETH Zürich)
|
|
|
Time-consistency of indifference prices and monetary utility functions
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. We
consider an agent endowed with a dynamic utility function (U_t) and an
initial endowment V. At each time t, his preferences are induced by a
utility function U_t being concave and monotone. Utility functions at
different times are linked in a consistent way which is called time- or
dynamic-consistency. The utility indifference bid price b_t of a claim
X is the price at which the agent is indifferent between paying nothing
and not having X and paying b_t and receiving X given the information
available at time t. It is the maximal price he is willing to pay for
the claim X at time t. We give necessary and sufficient conditions such
that the indifference bid prices satisfy a time-consistency property.
We also discuss representations for dynamic monetary utility functions.
It is joint work with Patrick Cheridito.
|
|
12.12.2005
|
Andrzej Ruszczynski (Rutgers University)
|
|
|
Risk-Averse Optimization
|
|
|
ETHZ, HG E41, 16:30-18:00 (Coffee 16:00-16:30)
|
|
|
Abstract. We
discuss stochastic optimization problems involving models of risk. At
first we focus on problems involving convex measures of risk and we
develop opt imality and duality theory for these models. Then we pass
to dynamic optimization problems with measures of risk and we present
dynamic programming theory for such problems. In the next part we
propose a new model involving stochastic dominance constraints with
respect to random benchmarks. We develop optimality and duality theory
for these models. We discuss connections of this model to the theories
of expected utility and rank dependent expected utility. Finally we
present an application to portfolio optimization.
|
|
08.12.2005
|
Marie Chazal (ETH Zürich)
|
|
|
Equilibrium Pricing Bounds on Option Prices
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
01.12.2005
|
Carlo Sgarra (Politecnico di Milano)
|
|
|
Equivalent martingale measures for Barndorff-Nielsen/Shephard models
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. The talk
will offer a survey on the main results available for Option Pricing
and Hedging in the framework of a class of Stochastic Volatility models
with Jumps introduced by O. Barndorff-Nielsen and N. Shephard. Some new
results obtained in the same context in two joint works with F. Hubalek
(Aarhus University, Denmark) will be provided.
|
|
30.11.2005
|
Jun Sekine (Kyoto University)
|
|
|
An asymptotic analysis for utility indifference price
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
(Seminar on Stochastic Processes)
|
|
17.11.2005
|
Nizar Touzi (CREST Paris and Imperial College London)
|
|
|
Second order BSDEs and fully nonlinear PDEs
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. Abstract.pdf
|
|
03.11.2005
|
Ying Hu (Université de Rennes 1)
|
|
|
Backward stochastic differential equations with quadratic growth with applications to finance and control
|
|
|
ETHZ, Hermann-Weyl-Zimmer, HG G43, 17.15 - 18.15
|
|
|
Abstract. In this talk, I'll first give some results concerning the
existence and uniqueness of solutions to backward stochastic
differential equations (BSDEs) with quadratic growth. In particuler,
I'll introduce the localization procedure developped for BSDEs. Then,
one application to utility maximization with nonconvex constraint is
given. The end of the talk will be devoted to another application to
the existence of stochastic optimal control.
|
|
|
Additional Material. paper1, paper2, paper3.
|
SS 05
Thursday, June 30, 2005,
17.15-18.15 h
(ETHZ, HG G26.3)
- Dieter Denneberg (Universität Bremen)
Title: Dependence values for allocation of risk capital and for
premium calculation
Abstract:
A class of dependence values for pairs of random variables is
introduced as a technical tool for the problem how the risk capital
needed for a portfolio of random activities should be allocated to it's
components. The well known allocation model with expected shortfall as
corresponding risk value is a prominent member of this class. Our
dependence values also apply to premium calculation within a portfolio
of dependent insurance branches.
(Seminar on Financial and Insurance Mathematics)
Thursday, June 16, 2005,
17.15-18.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
Title: Quantile Hedging for Risk-Management of Equity-Linked Life Insurance Contracts
Abstract
(Seminar on Financial and Insurance Mathematics)
Thursday, June 9, 2005,
17.15-18.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
- Stefan Weber
(Humboldt-Universität zu Berlin)
Title: Utility Maximization under Model Uncertainty with a Shortfall Risk Constraint
Abstract:
We consider the problem of utility maximization under model uncertainty
in the presence of both cost and risk constraints. Downside risk is
measured by utility-based shortfall risk.
We first review the
properties of utility-based shortfall risk. The acceptance sets of
these risk measures are defined in terms of a convex loss function and
a fixed threshold level.
Second, we discuss utility maximization
under both cost and risk constraints, if there is no model uncertainty.
By means of its dual problem, the optimization problem can explicitly
be solved.
Finally, we characterize the solution of the robust
utility maximization problem under robust constraints. In this case,
model uncertainty involves three aspects: the measurement of the
utility, the cost and the downside risk. We assume that investors take
a worst case approach.
The talk is based on joint work with Anne Gundel (Humboldt-Universität zu Berlin).
(Seminar on Financial and Insurance Mathematics)
Thursday, June 2, 2005,
17.15-18.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
- Marco Scarsini
(Università di Torino)
Title: Optimal Risk Sharing with Background Risk
Abstract:
We discuss the qualitative properties of efficient insurance contracts
in the presence of background risk. In order to get results for all
strictly risk averse expected utility maximizers, we use the concept of
“stochastic increasingness.” We show that different assumptions on the
stochastic dependence between the insurable and uninsurable risk lead
to different optimal contracts. We compare our results to the classical
results in the absence of background risk or to the case of independent
risks. The theory is further generalized to nonexpected utility
maximizers.
(Seminar on Financial and Insurance Mathematics)
Thursday, May 19, 2005,
17.15-18.15 h
(ETHZ, HG E33.5)
Title: Risk measure pricing and hedging in incomplete markets
Abstract:
This article attempts to extend the complete market option pricing
theory to incomplete markets. Instead of eliminating the risk by a
perfect hedging portfolio, partial hedging will be adopted and some
residual risk at expiration will be tolerated. The risk measure (or
risk indifference) prices charged for buying or selling an option are
associated to the capital required for dynamic hedging so that the risk
exposure will not increase. The associated optimal hedging portfolio is
decided by minimizing a convex measure of risk. We will give the
definition of risk-efficient options and confirm that options evaluated
by risk measure pricing rules are indeed risk-efficient. Relationships
to utility indifference pricing and pricing by valuation and stress
measures will be discussed. Examples using shortfall risk measure and
average VaR will be shown.
(Seminar on Financial and Insurance Mathematics)
Thursday, May 19, 2005,
16.00-17.00 h
(ETHZ, HG E33.5)
- Michael Schröder (Universität Mannheim)
Title: Constructive approaches to exponential functionals of Brownian motion,
and their applications to the explicit valuation of Asian options
Abstract:
Exponential functionals of Bronian motion have been studied in response
to questions in contingent claim valuation, and the valuation of Asian
options in particular. Building on work in particular of Yor's, new
insights into their structure have been obtained recently. Our talk
seeks to give a coherent account of the methods and the key results of
this development. Since these now finally are constructive as well, we
illustrate them by examples. We in particular discuss how our structure
theory thus finally enables the benchmark valuation of Asian options,
and, by means of Laguerre reduction series, moreover furnishes most
efficient methods for explicitly computing such values.
(Seminar on Financial and Insurance Mathematics)
Thursday, May 12, 2005,
17.15-18.15 h
(ETHZ, HG E33.5)
Title: Weather markets - overview, trends, pricing
(Seminar on Financial and Insurance Mathematics)
Thursday, May 12, 2005,
16.00-17.00 h
(ETHZ, HG E33.5)
Title: Loss Reserving and Hofmann Distributions
(Seminar on Financial and Insurance Mathematics)
Thursday, April 28, 2005,
17.15-18.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
- Marc Yor (Université Paris VI)
Title: Some representations of certain subordinations including the Gamma
processes as inverse local times of diffusions
(Seminar on Financial and Insurance Mathematics)
Thursday, April 21, 2005,
17.15-18.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
Title: Bivariate risk analysis for traders and the DAX
(Seminar on Financial and Insurance Mathematics)
Thursday, April 14, 2005,
17.15-18.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
- Fabio Trojani
(Universität St. Gallen)
Title: Learning and Asset Prices under Ambiguous Information
Abstract: We propose a new continuous-time framework to study asset
prices under learning and ambiguity aversion. In a partial information
Lucas economy with time-additive power utility, a discount for
ambiguity arises if and only if the relative risk aversion is below
one. Then, ambiguity increases equity premia and volatilities, and
lowers interest rates. In our setting, ambiguity does not resolve
asymptotically and, for low risk aversion, it is consistent with the
qualitative predictions of the equity premium, the low interest rate,
and the excess volatility puzzles.
(Seminar on Financial and Insurance Mathematics)
Thursday, April 7, 2005,
17.15-18.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
- Marco Frittelli
(Università degli Studi di Firenze)
Title: Risk measures and capital requirements for processes
Abstract: We propose a generalization of the concepts of convex and
coherent risk measures to a multi-period setting, in which payoffs are
spread over different dates. To this end, a careful examination of the
axiom of translation invariance and the related concept of capital
requirement in the one-period date is performed. These two issues are
then suitably extended to the multi-period case. A characterization in
terms of expected values is derived for this class of capital
requirements.
(Seminar on Financial and Insurance Mathematics)
