Talks in Financial and Insurance Mathematics

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

Spring Semester 2015

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
5 February 2015
Johannes Ruf
Oxford-Man Institute of Quantitative Finance
A Numeraire-Independent Version of the Fundamental Theorem of Asset Pricing  HG G 43 
Abstract: The Fundamental Theorems of Asset Pricing are aptly-named results that show the relationship between absence of arbitrage and the martingale property. These theorems are fundamental to mathematical finance in that they provide the bridge between the mathematics and the finance: on the one side, the mathematical objects of stochastic processes and martingale measures; on the other the financial ideas of trading strategies and arbitrage. We aim to widen the bridge to cover cleanly the case when there are multiple financial assets, any of which may potentially lose all value relative to the others. To do this we shift away from having a pre-determined numeraire to a more symmetrical point of view where all assets have equal priority. Joint work with Travis Fisher and Sergio Pulido.
19 February 2015
Edward Furman
York University, Canada
Paths and indices of maximal tail-dependence  HG G 43 
Abstract: I will hint that the existing methods for measuring tail dependence in copulas may sometimes underestimate the extent of extreme co-movements of dependent risks and, therefore, may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the context of both symmetric and asymmetric copulas with and without singularities. As a remedy, I will introduce a notion of paths of maximal (tail) dependence and utilize it to propose several new indices of tail dependence. The suggested new indices are conservative, conform with the basic concepts of modern quantitative risk management, and are able to distinguish between distinct risky positions in situations when the existing indices fail to do so. This is a joint work with Jianxi Su of York University and Ricardas Zitikis of the University of Western Ontario.
* 24 February 2015
Jan Kallsen
Universität Kiel
On portfolio optimization with small transaction costs: some recent results  HG G 43 
Abstract: Portfolio optimization problems with frictions as e.g. transaction costs are hard to solve explicitly. In the limit of small costs, solutions are often of much simpler structure. In the last twenty years, considerable progress has been made both in order to derive formal asymptotics as well as rigorous proofs. In this talk we discuss some recent results, in particular on fixed costs.
* 25 February 2015
Ben Berckmoes
University of Antwerp
Approach theory in mathematical statistics  HG G 43 
Abstract: Approach theory is a topological theory which constitutes the canonical framework for the development of indices which measure up to what extent topological properties are valid. The theory has in the last years reached a degree of maturity allowing it to be applied in various branches of mathematical analysis, including probability theory and mathematical statistics. In this talk we give an introduction to approach theory and explain how it is connected to probability theory through so-called quantitative central limit theory. We also give a first statistical application by looking at the asymptotic behavior of the sample mean with contaminated observations.
16 April 2015
Artem Neklyudov
Université de Lausanne
Bid-Ask Spreads and the Over-the-Counter Interdealer Markets: Core and Peripheral Dealers  HG G 43 
Abstract: This paper studies how the coexistance of dealers with different search technologies on an over-the-counter (OTC) market affects asset pricing, customer bid-ask spreads, interdealer trade volumes, and efficiency of asset allocation. Empirical evidence suggests that dealer networks on OTC markets for corporate bonds, municipal bonds, and securitizations have a core-peripheral structure, and that terms of trade for customers depend on whether customers trade with core dealers or peripheral dealers. The paper shows that, on OTC markets, differences in the trade execution efficiency between core dealers and peripheral dealers can explain the observed differences in customer pricing and the observed interdealer trade patterns.
23 April 2015
Jonathan Donier
Université Paris 6 & CFM
How agents' decisions impact prices: Empirical evidence, theory and implications  HG G 43 
Abstract: The non linear impact of agents' decisions on market prices is arguably one of the main puzzles that arise when it comes to unraveling the price formation mechanism on (non-)financial markets. Supported by strong evidence from the Bitcoin market, we develop a reaction-diffusion model that consistently accounts for most empirical facts known so far on price impact, thus resolving the apparent "square root impact law" paradox and laying new foundations for addressing common impact-related problems (among which, agent-based modelling, trading costs minimization and monitoring of market liquidity and stability).
30 April 2015
Christa Cuchiero
Universität Wien
A General HJM Framework for Multiple Yield Curve Modeling  HG G 43 
Abstract: We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS forward rates, which also have an interpretation in terms of a foreign exchange analogy. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor’s length. When the driving semimartingale is an affine process, we obtain a flexible and tractable Markovian structure. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling. The talk is based on joint work with Claudio Fontana and Alessandro Gnoatto.
7 May 2015
Fred Espen Benth
University of Oslo
Stochastic volatility in energy forward prices  HG G 43 
Abstract: We propose an infinite-dimensional version of the Barndorff-Nielsen and Shephard stochastic volatility model, and apply it to forward pricing in energy markets. Some properties of Hilbert space valued Ornstein-Uhlenbeck processes are studied, like the characteristic functional.
* 12 May 2015
Yavor Stoev
London School of Economics
Equilibrium with imbalance of the derivative market  HG G 43 
Abstract: We investigate the impact of imbalanced derivative markets - markets in which not all agents hedge - on the underlying stock market. The availability of a closed-form representation for the equilibrium stock price in the context of a complete (imbalanced) market with terminal consumption allows us to study how this equilibrium outcome is affected by the risk aversion of agents and the degree of imbalance. In particular, it is shown that the derivative imbalance leads to significant changes in the equilibrium stock price process: volatility changes from constant to local, while risk premia increase or decrease depending on the replicated contingent claim, and become stochastic processes. Moreover, the model produces implied volatility smile consistent with empirical observations.
14 May 2015
Ascension day
* 21 May 2015
Marcel Nutz
Columbia University
Optimal Transport and Robust Finance  HG G 19.2 
Abstract: After a brief introduction to classical optimal transport, we shall focus on the so-called martingale optimal transport and its connection to finance, the problem of robust semi-static hedging. Some differences with the classical transport problem will be highlighted, in particular the failure of duality in the usual sense. We explain how to obtain a complete duality theory using notions related to Knightian uncertainty about pricing models. Based on joint work with Mathias Beiglböck and Nizar Touzi.
21 May 2015
Adrian Buss
Trading Fees and Slow-Moving Capital  HG G 43 
Abstract: In some situations, investment capital seems to move slowly towards profitable trades. We develop a model of a financial market in which capital moves slowly simply because there is a proportional cost to moving capital. We incorporate trading fees in an infinite-horizon dynamic general-equilibrium model in which investors optimally and endogenously decide when and how much to trade. We determine the steady-state equilibrium no-trade zone, study the dynamics of equilibrium trades and prices and compare, for the same shocks, the impulse responses of this model to those of a model in which trading is infrequent because of investor inattention.
28 May 2015
Claude Martini
Zeliade Systems
Martingale measures with given marginals: extremal points and perturbations  HG G 43 
Abstract: The extremal points in the set of all measures with pre-specified marginals, without the martingale constraint, have been extensively studied by many authors in the past (e.g. Douglas, Letac, Denny, Klopotowski to cite only a few). In this talk, we will focus on the characterization provided by Denny in the countable case: a key property is that the support of the probability Q has no “cycle”, otherwise a perturbation of Q can be constructed so that Q can not be extremal. In the context of the 2 marginals martingale problem we give an analogous "cycle-like" property that corresponds to martingale perturbations and investigate in detail the support of extremal points in the countable case.
11 June 2015
Tony Ware
University of Calgary
Splitting methods and energy derivative pricing  HG G 43 
Abstract: Operator splitting methods form a staple part of our arsenal of approaches to the numerical solution of PDEs. They work by a `divide and conquer' approach, reducing a complex problem to a sequence of simpler problems, which confers advantages when it comes to designing, coding and analyzing algorithms. We discuss some uses of operator splitting methods for certain types of Hamilton-Jacobi-Bellman equations arising in energy derivative pricing, and describe in detail an example relating to gas storage valuation. We will also illustrate how operator splitting can be used to extend the applicability of existing methods to more complex settings; for example, we show how, through the use of splitting, Fourier methods can be applied to valuation problems with non-constant coefficients or in high dimensional settings.
* 15 June 2015
Hansjoerg Albrecher
Université de Lausanne
On Optimal Dividend Strategies for Two Collaborating Insurance Companies  HG G 43 
Abstract: In this talk a two-dimensional optimal dividend problem in the context of two insurance companies is considered. The companies collaborate by paying each other’s deficit when possible. Extending results of univariate optimal control theory, the problem of maximizing the weighted sum of expected discounted dividend payments until ruin of both companies is studied. Comparisons of the optimal solution to the alternative of merging the two companies or to optimize dividends on a stand-alone basis are illustrated by way of example (based on joint work with P. Azcue and N. Muler).
18 June 2015
Antoine Jacquier
Imperial College London
Variations on the Heston Theme  HG G 43 
Abstract: The Heston model is one of the most popular stochastic volatility models used in mathematical finance, both in academia and by practitioners. Calibration on (Equity) implied volatility surfaces usually exhibit a good fit and the affine structure of the model makes it very amenable to option pricing. However, both the short-term smile and the VIX smile are notoriously mis-calibrated. We propose here variations of the Heston model, which we call "randomised (Heston) volatility models"; these variations, still with continuous paths, preserve the affine structure while allowing for better small-maturity asymptotic behaviour and are more consistent with the behaviour of the VIX smile.
* 25 June 2015
Andrew Lo
Evolutionary Foundations of Economic Behavior, Bounded Rationality, and Intelligence  HG E 1.1 
Abstract: In a simple evolutionary model with one-period agents that make binary choices which determine their reproductive success, we show that natural selection is capable of generating several behaviors that have been observed in organisms ranging from ants to human subjects, including risk-sensitive foraging, risk aversion, loss aversion, probability matching, randomization, and diversification. Given an initial population of individuals, each assigned a purely arbitrary behavior with respect to a binary choice problem, and assuming that offspring behave identically to their parents, only those behaviors linked to reproductive success will survive, and less reproductively successful behaviors will disappear at exponential rates. When the uncertainty in reproductive success is systematic, natural selection yields behaviors that may be individually sub-optimal but are optimal from the population perspective; when reproductive uncertainty is idiosyncratic, the individual and population perspectives coincide. The simplicity and generality of our model imply that these derived behaviors are primitive and universal within and across species. This framework also suggests a natural definition of intelligence---any behavior positively correlated with reproductive success---and links physiological and environmental constraints to the degree of intelligence that emerges, i.e., bounded rationality.
2 July 2015
Stefan Waldenberger
TU Graz
Extension of affine market models  HG G 43 
Abstract: The class of affine LIBOR models is appealing since it satisfies three central requirements of interest rate modeling. It is arbitrage-free, interest rates are nonnegative and caplet and swaption prices can be calculated analytically. In order to guarantee nonnegative interest rates affine LIBOR models are driven by nonnegative affine processes, a restriction, which makes it hard to produce volatility smiles. The first part of the talk presents a modification of the affine LIBOR models, so that real-valued affine processes can be used without destroying the nonnegativity of interest rates. Numerical examples show that in this class of models pronounced volatility smiles are possible. The second part then extends the affine LIBOR models to inflation markets. Due to the highly tractable structure of the model prices for all standard inflation derivatives can be calculated analytically. A calibration example shows that the model can reproduce market-observed prices very accurately.

Organizers: Paul Embrechts , Martin Schweizer , Halil Mete Soner , Josef Teichmann , Mario Valentin Wüthrich 

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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