Talks in Financial and Insurance Mathematics

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This is the regular weekly research seminar on Insurance Mathematics and Stochastic Finance.

Autumn Semester 2012

Note: The highlighted event marks the next occurring event and events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Date / Time Speaker Title Location
6 September 2012
Prof. Dr. Ales Cerny
City University London
Optimal Hedging With Higher Moments (joint work with Chris Brooks, Reading and Joelle Miffre, EDHEC Nice, to appear in Journal of Futures Markets)  HG G 43 
Abstract: The study proposes a utility-based framework for the determination of optimal hedge ratios that can allow for the impact of higher moments on hedging decisions. We examine the entire hyperbolic absolute risk aversion (HARA) family of utilities which include quadratic, logarithmic, power and exponential utility functions. We provide an illustration of our methodology using an example of a passenger airline hedging its fuel exposure. We find that for both moderate and large spot (commodity) exposures, the performance of out-of-sample hedges constructed allowing for non-zero higher moments is better than the performance of the simpler OLS hedge ratio. The picture is, however, not uniform throughout our seven spot commodities as there is one instance (cotton) for which the modeling of higher moments decreases welfare out-of-sample relative to the simpler OLS. We support our empirical findings by a theoretical analysis of optimal hedging decisions and we uncover a novel link between optimal hedge ratios and the minimax hedge ratio, that is the ratio which minimizes the largest loss of the hedged position.
14 September 2012
Risk Day  HG E 5 
Abstract: Mini-Conference on Risk Management in Finance and Insurance.
27 September 2012
No Talk - Delbaen Conference
4 October 2012
Prof. Dr. Steven Shreve
University Carnegie Mellon, USA
A diffusion limit of a limit-order book model  HG G 3 
Abstract: Stock trading today occurs almost entirely on electronic exchanges. While the first of electronic exchange, NASDAQ, was founded in 1971, most such exchanges have appeared within the past fifteen years. Even traditional exchanges, such as the NYSE, are now predominantly electronic. Electronic exchanges maintain limit-order books, which evolve rapidly in time. A limit-order announces the desire to buy (or sell) a certain number of share of a stock at a particular price or lower (higher). If there is no matching order on the exchange at this or a better price, an arriving limit-order is queued for later execution or possible cancellation by the submitting agent. A limit-order book is thus a set of queues at each price with the size of the queue denoting the number of shares available at that price and the sign of the length denoting whether the orders are buy or sell. In this talk we consider a model for limit-order book dynamics and discuss its diffusion limit. This is joint work with John Lehoczky and Christopher Almost.
11 October 2012
Prof. Dr. Jin-Chuan Duan
National University of Singapore
Price and Volatility Dynamics Implied by the VIX Term Structure  HG G 43 
Abstract: A particle-filter based estimation method is developed for the stochastic volatility model with/without jumps and applied on the S&P 500 index value and the VIX term structure jointly. The model encompasses all mean-reverting stochastic volatility option pricing models with a constant elasticity of variance, and can allow for price jumps. Our contention is that using the VIX term structure in estimation can help reach a more reliable conclusion on the nature of the risk-neutral volatility dynamic. Our empirical findings are: (1) the volatility process under the risk-neutral measure is mean-reverting; (2) the jump intensity is time-varying; (3) the jump and volatility risks are priced; (4) the measurement errors in VIXs are material; and (5) the square-root volatility process is mis-specified with or without price jumps.
18 October 2012
Curdin Ott
University of Bath, UK
Capped Optimal Stopping Problems for the Maximum Process  HG G 43 
Abstract: This talk concerns optimal stopping problems driven by a spectrally negative Levy process X. More precisely, we will consider capped versions of the Russian and American lookback optimal stopping problem and provide semi-explicit solutions in terms of scale functions. In particular, it turns out that the form of the solution changes qualitatively according to the path variation of X. Furthermore, we will link these capped problems to Peskir's maximality principle.
* 6 November 2012
Prof. Dr. Erhan Bayraktar
University of Michigan, USA
On the Multi-Dimensional Controller and Stopper Games  HG G 19.1 
Abstract: We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the volatility terms of the state process. Under appropriate conditions, we show that the game has a value and the value function is the unique viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation. Joint work with Yu-Jui Huang. Available at
* 6 November 2012
Prof. Dr. Tom Hurd
McMaster University, Canada
Cascade Models for Random Financial Networks  HG G 19.1 
Abstract: In 2001, Eisenberg and Noe put forward a simple accounting framework for analyzing default cascades in a deterministic financial network. Subsequent work has pushed the framework in many directions, notably in making more and more of its parts stochastic to reflect the numerous sources of uncertainty in our observations of real world networks. After reviewing some of the important variations that motivate the development of new mathematical techniques, I focus on a classic model from network science, the Watts 2002 Cascade Model. The basic structure of this threshold model is so universal that it has been used to understand such diverse phenomena as disease transmission, the spread of rumours and fads, the evolution of species, the collapse of power systems and avalanches in sandpile models. Its underlying simplicity will allow me to spend the remainder of the talk exposing some of the beautiful mathematical properties that lie buried within.
8 November 2012
Prof. Dr. Frank Riedel
Universität Bielefeld, Germany
The Basic Theorems of Finance under Model Uncertainty  HG G 43 
Abstract: In recent years, the discussion of model uncertainty, risk measures, and the emphasis on Knightian (non--probabilistic) uncertainty, has challenged the traditional approach to asset pricing. In the light of this development, we go back to the very foundations of asset pricing. In a discrete model, one does not need a probability measure on the state space to derive the fundamental theorem of asset pricing. The treatment of uncertainty in general equilibrium theory in the style of Arrow and Debreu does not require a prior probability on the state space neither. Finance models nevertheless treat payoffs as random variables, implicitly or explicitly using a known probability distribution. In the talk,we first explore the possibility to derive the fundamental theorem in a purely measure theoretic setup. The pricing functional given by an arbitrage--free market can be identified with a \emph{full support} martingale measure (instead of \emph{equivalent} martingale measure). We relate the no arbitrage theory to economic equilibrium by establishing a variant of the Harrison--Kreps--Theorem on viability and no arbitrage. Finally, we consider (super)hedging of contingent claims and embed it in a classical infinite--dimensional linear programming problem. The second part of the talk goes an intermediate step in between complete Knightain uncertainty and probability--based models by looking at the foundations of finance in the framework of Shige Peng's G--expectation theory.
22 November 2012
Elena Di Bernardino
University of Paris X
A multivariate extension of Value-at-Risk and Conditional-Tail-Expectation  HG G 43 
Abstract: In this paper, we introduce a multivariate extension of the classical univariate Value-at-Risk. This extension may be useful to understand how solvency capital requirement computed for a given financial institution may be affected by the presence of additional risks. We also generalize the bivariate Conditional-Tail-Expectation (CTE), previously introduced by Di Bernardino et al. (2011), in a multivariate setting and we study its behavior. Several properties have been derived. In particular, we show that these two risk measures both satisfy the positive homogeneity and the translation invariance property. Comparison between univariate risk measures and components of multivariate VaR and CTE are provided. We also analyze how they are impacted by a change in marginal distributions, by a change in dependence structure and by a change in risk level. Interestingly, these results turn to be consistent with existing properties on univariate risk measures. Illustrations are given in the class of Archimedean copulas.
29 November 2012
Torsten Schöneborn
Deutsche Bank
Optimal Liquidation in Dark Pools  HG G 43 
Abstract: Joint work with Peter Kratz Humboldt University of Berlin; Universit\'e d'Aix et de Marseille) Electronic trade execution is rapidly growing both commercially and as an academic research field. In this talk, we consider trading in dark pools, a relatively recent addition to the electronic trading landscape. More specifically, we consider a finite time horizon, multi-asset optimal liquidation problem in discrete time for an investor having access to both a traditional trading venue and a dark pool. Our model captures the price impact of trading in transparent traditional venues as well as the execution uncertainty of trading in a dark pool. We prove existence and uniqueness of optimal trading strategies for risk averse mean-variance-like traders and find that dark pools change optimal trading strategies and can significantly reduce trading costs. Their effect can be reduced by adverse selection and trading restrictions. In addition to the academic perspective we will briefly consider challenges and recent developments in the field from a practical point of view.
4 December 2012
Workshop on Robust Optimization in Finance: Opening Remarks HG G 19.1 
4 December 2012
Prof. Dr. Bernt Øksendal
University of Oslo
Workshop on Robust Optimization in Finance: A stochastic control approach to duality and robust duality in finance  HG G 19.1 
Abstract: A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities: (i) The optimal terminal wealth X*(T) : = X_{\phi*}(T) of the classical problem to maximise the expected U-utility of the terminal wealth X_{\phi}(T) generated by admissible portfolios \phi(t); 0≤t ≤T ; T in a market with the risky asset price process modelled as a semimartingale (ii) The optimal scenario dQ*/dP of the dual problem to minimise the expected V-value of dQ/dP over a family of equivalent local martingale measures Q. Here V is the convex dual function of the concave function U. (1) In the first part of this talk we consider markets modelled by Itô-Lévy processes, and we present a new approach to the above result in this setting, based on the maximum principle in stochastic control theory. An advantage with with our approach is that it also gives an explicit relation between the optimal portfolio \phi* and the optimal scenario Q*, in terms of backward stochastic differential equations. This is be used to obtain a general formula for the optimal portfolio \phi*(t) in terms of the Malliavin derivative. (2) In the second part of the talk we extend this approach to study robust optimal portfolio problems and their (robust) dual. We illustrate the results by examples. The presentation is based on recent joint work with Agnès Sulem, INRIA-Rocquencourt, Paris.
4 December 2012
Prof. Dr. Gregor Svinland
Ludwig-Maximilians-Universität München
Workshop on Robust Optimization in Finance: Pareto Optimal Allocations for Law-Invariant Robust Utilities  HG G 19.1 
Abstract: We prove the existence of Pareto optimal allocations if the involved agents have preferences in the class of probabilistic sophisticated variational preferences and thus choice criteria which correspond to law-invariant robust utilities.
4 December 2012
Prof. Dr. Alex Schied
Universität Mannheim
Workshop on Robust Optimization in Finance: Trading under transient price impact  HG G 19.1 
Abstract: Based on an idealized model of a limit order book with resilience, Obizhaeva & Wang (2005) were the first to analyze optimal portfolio liquidation trajectories under transient price impact. Their original model has been generalized in several ways, e.g., so as to include nonlinear price impact, nonexponential resilience, multiple assets, or additional drift. In this talk, we will review some of these extensions and discuss the optimisation problems arising in the corresponding portfolio liquidation problems. Particular emphasis will be given to the role played by a drift in asset prices. It turns out that this latter problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. This has some consequences on a two-player situation.
4 December 2012
Krzysztof Paczka
University of Oslo
Workshop on Robust Optimization in Finance: G-Lévy processes and robust optimization  HG G 19.1 
Abstract: In the talk I will present robust optimization using the G-Levy process with finite activity living in the sublinear expectation space. The Ito calculus, Ito formula and (FB)SDE's will be introduced. At the end of the talk I will relate the control of FBSDE's driven by a G-L'evy process to the standard theory via the representation theorem for sublinear expectation. Talk based on a research with An Ta (UiO).
5 December 2012
Prof. Dr. Agnès Sulem
Workshop on Robust Optimization in Finance: Stochastic control under Model uncertainty and Forward-Backward Stochastic differential equations.  HG G 43 
Abstract: TBA
5 December 2012
Prof. Dr. Michael Kupper
Humboldt Universität Berlin
Workshop on Robust Optimization in Finance: Minimal Supersolutions of BSDEs and Model Uncertainty  HG G 43 
Abstract: We discuss the existence and uniqueness of minimal supersolutions of BSDEs under model uncertainty when the probability models are not dominated by a reference probability measure. The talk is based on joint works with Samuel Drapeau and Gregor Heyne.
5 December 2012
Prof. Dr. Jan Obloj
University of Oxford
Workshop on Robust Optimization in Finance: Beyond one marginal: on various ways to incorporate more information into the robust pricing and hedging  HG G 43 
Abstract: In this talk we discuss some of recent and ongoing work related to using market information to make robust framework more efficient. We give example of incorporating prices of call options for multiple maturities as well as some historic time series of prices. Links with some recent works on no-duality results are mentioned.
5 December 2012
Peter Spoida
University of Oxford
Workshop on Robust Optimization in Finance: Maximum Maximum of Martingales given Marginals and an Iteration of the Azema-Yor Embedding  HG G 43 
Abstract: We propose a robust superhedging strategy for simple barrier options, consisting of a portfolio of calls with different maturities and a self-financing trading strategy. The superhedging strategy is derived from a pathwise inequality. We illustrate how a stochastic control ansatz can provide a good guess for finding such strategies. Under some additional assumption we construct a worst-case model - a solution to the Skorokhod embedding problem - hence demonstrating that our superhedge is the cheapest possible. A discussion of extensions of this embedding is provided. The talk is based on joint work with Pierre Henry-Labordere, Jan Obloj and Nizar Touzi.
5 December 2012
Dr. An Thi Kieu Ta
University of Oslo
Workshop on Robust Optimization in Finance:Optimal stopping problem under ambiguity with jumps  HG G 19.2 
Abstract: In this paper we study an optimal stopping problem under ambiguity associated with jump--diffusion processes. We use a viscosity solution approach for the solution to HJB equality. We show how to use these results for search problems and American options.
5 December 2012
Prof. Dr. Halil Mete Soner 
ETH Zurich, Switzerland
Workshop on Robust Optimization in Finance: Robust Hedging and Martingale Optimal Transport HG G 19.2 
5 December 2012
Workshop on Robust Optimization in Finance: Closing Remarks HG G 19.2 
13 December 2012
Prof. Dr. Xunyu Zhou
The Equity Premium and Risk-Free Rate Puzzles: Perspective from Rank-Dependent Utility Theory  HG G 43 
Abstract: We examine the classical equity premium and risk-free rate puzzles from the rank-dependent utility (RDU) theory. After establishing the equilibrium and pricing theory for an RDU economy, we find that the presence of probability weighting provides a right direction in explaining the puzzles.

Organizers: Winslow Strong

Archive: SS 17  AS 16  SS 16  AS 15  SS 15  AS 14  SS 14  AS 13  SS 13  AS 12  SS 12  AS 11  SS 11  AS 10  SS 10  AS 09 

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