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 2014

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
30 January 2014
Prof. Dr. Eberhard Mayerhofer
Dublin City University (DCU)
The Limits of Leverage  HG G 43 
Abstract: If trading incurs proportional costs, leverage can scale the return of an asset only up to a maximum multiple, which is sensitive to the asset’s volatility and liquidity. In a model with one safe and one risky asset, with constant investment opportunities and proportional transaction costs, we find the family of mean-variance efficient portfolios. As leverage and volatility increase, rising rebalancing costs imply a declining Sharpe ratio. Beyond a critical level, even the expected return declines. We derive the optimal tradeoff between high alpha and low tracking error for funds that seek to replicate multiples of index returns, such as leveraged ETFs.
6 February 2014
Prof. Dr. Min Dai
Dept. of Math. and Centre for Quantitative Finance, National University of Singapore
Asymptotics for Merton Problem with Small Capital Gain Tax and Interest Rate  HG G 43 
Abstract: We consider the continuous-time optimal investment and consumption decision of a constant relative risk aversion investor who faces capital gain taxes. It is shown by Ben Tahar et al. (2010) that the problem reduces to the classical Merton problem as the interest rate vanishes. We present asymptotic expansions with small interest rate and tax rate. Our expansions offer a good approximation of the optimal buy and sell boundaries for small interest rate and tax rate. Numerical results are presented to demonstrate our theoretical analysis. This work is jointly with Xinfu Chen.
27 February 2014
Dr. Dylan Possamaï
École Polytechnique
Moral Hazard in Dynamic Risk Management  HG G 43 
Abstract: We consider a contracting problem in which a principal hires an agent to manage a risky project. When the agent chooses volatility components of the output process and the principal observes the output continuously, the principal can compute the quadratic variation of the output, but not the individual components. This leads to moral hazard with respect to the risk choices of the agent. Using a very recent theory of singular changes of measures for Ito processes, we formulate the principal-agent problem in this context, and solve it in the case of CARA preferences. In that case, the optimal contract is linear in these factors: the contractible sources of risk, including the output, the quadratic variation of the output and the cross-variations between the output and the contractible risk sources. Thus, path-dependent contracts naturally arise when there is moral hazard with respect to risk management. This is a joint work with Nizar Touzi (CMAP, Ecole Polytechnique) and Jaksa Cvitanic (Caltech).
6 March 2014
Dr. Janusz Milek
Zurich Insurance Company
A copula family for risk capital aggregation  HG G 43 
Abstract: Some known copula families like Gauss, t, or Archimedean may in certain situations be inappropriate for risk capital modeling. In this talk, a potentially suitable copula family is discussed, which (i) is relatively simple, (ii) covers a wide range of tail dependence structures, and (iii) does not introduce countermonotonicity. In addition, the copula-based aggregate is, under particular conditions, related to the Variance-Covariance (VC) aggregate, so the copula can be considered as a multivariate simulation counterpart of the well-established VC method. The copula family being discussed is a convex combination of particular "canonical" copulas, the cardinality of which grows quickly with the copula dimension. Calibration of the underlying (canonical) structure to a given bivariate or even multivariate tail dependence structure can be performed via linear or quadratic programming. A sparse parameterization technique that reduces the number of parameters and ensures calibration feasibility for larger copula dimensions can be implemented via nonlinear programming. A method for deriving a set of necessary and sufficient conditions for realization of bivariate and multivariate dependence structures is presented. An example is available, which demonstrates ability of the copula to realize a given tail dependence structure where Joe’s feasibility conditions become sharp and which cannot be realized using t (and possibly also Archimedean) families. A Kronecker convolution method is discussed which simplifies parameterization and construction of higher dimensional copulas by combining low dimensional copulas, such that the resulting tail dependence structure is a Kronecker product of the tail dependence structures of the low dimensional copulas.
13 March 2014
Guillaume Royer
École Polytechnique
Liquidation of an indivisible asset with independent investment  HG G 43 
Abstract: We provide an extension of the explicit solution of a mixed optimal stopping-optimal stochastic control problem introduced by Henderson and Hobson. The problem examines whether the optimal investment problem on a local martingale financial market is affected by the optimal liquidation of an independent indivisible asset. The indivisible asset process is defined by a homogeneous scalar stochastic differential equation, and the investor's preferences are defined by a general expected utility function. The value function is obtained in explicit form, and we prove the existence of an optimal stopping--investment strategy characterized as the limit of an explicit maximizing strategy. Our approach is based on the standard dynamic programming approach. Reference: V. Henderson and D. Hobson (2008): An explicit solution for an optimal stopping/optimal control problem which models an asset sale. Annals of Applied Probability 18(5), 1681-1705.
* 18 March 2014
Prof. Dr. Michael Mania
A. Razmadze Mathematical Institute of Tbilisi State University, Georgia
On the properties of the dynamic value functions in the problem of optimal investing in incomplete markets  HG G 43 
Abstract: We study analytical properties of the dynamic value function and of the optimal wealth process to the utility maximization problem in incomplete markets, where the dynamics of asset prices are described by a continuous semimartingale satisfying the structure condition. Under some regularity assumptions on the utility function defined on the whole real line, we show that the value function related to the utility maximization problem is a regular parameterized family of semimartingales. These properties we then use to show that the value function satisfies a certain backward stochastic partial differential equation, which enables us to characterize the optimal wealth process. The talk is based on the joint work with Revaz Tevzadze
20 March 2014
Dr. Martin Larsson
EPF Lausanne
Polynomial preserving diffusions and models of the term structure  HG G 43 
Abstract: Polynomial preserving processes are multivariate Markov processes that extend the important class of affine processes. They are defined by the property that the semigroup leaves the space of polynomials of degree at most $n$ invariant, for each $n$, which lends significant tractability to models based on these processes. In this talk I will discuss existence and uniqueness of polynomial preserving diffusions, a task which is made nontrivial due to degenerate and non-Lipschitz diffusion coefficients, as well as a complicated geometric structure of the state space. I will also describe how polynomial preserving processes can be used to build term structure models that accommodate three features that are otherwise difficult to combine: nonnegative short rates, tractable swaption pricing, and unspanned factors affecting volatility and risk premia.
17 April 2014
Prof. Dr. Vygantas Paulauskas
Vilnius University
On α-covariance, long, short and negative memories for sequences of random variables with infinite variance  HG G 43 
Abstract: In the talk we consider a measure of dependence for symmetric α-stable random vectors, which was introduced by the author in 1976. We demonstrate that this measure of dependence can be extended for much more broad class of random vectors (up to regularly varying vectors in separable Banach spaces). This measure is applied for linear random processes and fields with heavy-tailed innovations, for some stable processes, and these applications show that this dependence measure, named as α-covariance, is a good substitute for the usual covariance. Also we discuss a problem of defining long, short, and negative memories for stationary processes and fields with infinite variances.
1 May 2014
Labour Day
15 May 2014
Prof. em. Dr. Alois Gisler 
ETH Zurich, Switzerland
Der rasante Einzug der Mathematik in der Nicht-Lebensversicherung: Eine Zeitreise über 40 Jahre  HG F 30 
Abstract: Farewell lecture with subsequent aperitif in the Dozentenfoyer (J Floor). The presentation will be given in German.
22 May 2014
Prof. Dr. Chris Rogers
University of Cambridge
Diverse beliefs and diverse information  HG G 43 
Abstract: The main result of this talk is that a finite-horizon discrete-time DSGE where agents have diverse information is observationally equivalent to one where the agents have diverse beliefs. This is important because diverse beliefs models are quite easy to study, diverse information models are not.
12 June 2014
Kevin Webster
The self-financing equation in high-frequency markets  HG G 43 
Abstract: High Frequency Trading (HFT) represents an ever growing proportion of all financial transactions as most markets have now switched to electronic order book systems. The main goal of the paper is to propose continuous time equations which generalize the self-financing relationships of frictionless markets to electronic markets with limit order books. We use NASDAQ ITCH data to identify significant empirical features such as price impact and recovery, rough paths of inventories and vanishing bid-ask spreads. Starting from these features, we identify microscopic identities holding on the trade clock, and through a diffusion limit argument, derive continuous time equations which provide a macroscopic description of properties of the order book. These equations naturally differentiate between trading via limit and market orders. We give several applications (including hedging European options with limit orders, market maker optimal spread choice, and toxicity indexes) to illustrate their impact and how they can be used to the benefit of Low Frequency Traders (LFTs). (joint work with Rene Carmona)
26 June 2014
Prof. Dr. Robert Stelzer 
Universität Ulm
Infinitely divisible multivariate and matrix Gamma distributions  HG G 43 
Abstract: Classes of multivariate and cone valued infinitely divisible Gamma distributions are introduced. Particular emphasis is put on the cone-valued case, due to the relevance of infinitely divisible distributions on the positive semi-definite matrices in applications. The cone-valued class of generalised Gamma convolutions is studied. In particular, a characterisation in terms of an Itô–Wiener integral with respect to an infinitely divisible random measure associated to the jumps of a Lévy process is established. A new concrete example of an infinitely divisible positive definite Gamma random matrix is thereafter introduced. It has properties which makes it appealing for modelling, e.g. an interesting relation of the moments of the Lévy measure and the Wishart distribution can be shown. Finally, we discuss possible multivariate variance Gamma distributions.
* 17 July 2014
Prof. Dr. Romuald Elie
Université Paris-Est Marne-la-Vallée
Hedging and pricing under portfolio constraint  HG G 43 
Abstract: This talk deals with the super-replication of non path-dependent European claims under additional convex constraints on the number of shares held in the portfolio. The corresponding super-replication price of a given claim has been widely studied in the literature and its terminal value, which dominates the claim of interest, is the so-called facelift transform of the claim. We investigate under which conditions the super-replication price and strategy of a large class of claims coincide with the exact replication price and strategy of the facelift transform of this claim. This question relates to viability properties for BSDEs. We next investigate the regularity of the portfolio constrained super-replication price in general and introduce a probabilistic numerical scheme in order to compute it. This talk is based on joint works with Bruno Bouchard, Jean-François Chassagneux, Idris Kharroubi and Ludovic Moreau.
17 July 2014
Prof. Dr. Yan Dolinsky
Hebrew University, Jerusalem
Risk Minimization in Markets Imposing Minimal Transaction Costs  HG G 43 
Abstract: We study partial hedging in markets with transaction costs bounded from below. More precisely, we assume that the investor's transaction costs for each trade are the minimum between proportional transaction costs and a fixed transaction costs. We prove that in the continuous time Black--Scholes (BS) model, there exists a trading strategy which minimizes the shortfall risk. Furthermore, the trading strategy is given by a dynamical programming. joint work with Y.Kifer.

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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