One-Day Workshop on Portfolio Risk Management
sponsored by the Vienna Science and Technology Fund (WWTF)
|9:10-10:00||Prof. Dr. Saul Jacka
(Department of Statistics, University of Warwick)
(Partial) Hedging for Coherent Risk Measures
Abstract: The talk will consider problems of hedging for a market maker who prices with respect to coherent risk measures including the hedging/reserving problem for an intermediate market maker.
|10:30-11:20||Dr. Michael Kupper
(Operations Research and Financial Engineering, Princeton University)
Dynamic Monetary Utility Functions
Abstract: If the random future evolution of discounted values is modeled in discrete time, a monetary utility function can be viewed as a function on the space of all bounded stochastic processes which are adapted to a given filtration. Calculating the utility at each time t leads to the notion of a process of monetary utility functions. We study time-consistency properties of processes of monetary utility functions for finite and infinite time horizon. It turns out that time-consistency is equivalent to the property that the corresponding acceptance sets are decomposable in time. For processes of coherent and concave monetary utility functions admitting a robust representation with sigma-additive linear functionals, we give necessary and sufficient conditions for time-consistency in terms of the representing functionals. We also give a new representation for processes of concave monetary utility functions, which is based on the decomposition of the acceptance set in the one-time-step acceptance sets. This new representation allows us to construct multi-period utility functions. Some examples are discussed. It is joint work with Patrick Cheridito and Freddy Delbaen.
(Department of Mathematics for Decisions, University of Firenze)
Bounds for Functions of Multivariate Risks
Abstract: Li et al. [Distributions with Fixed Marginals and Related Topics, vol. 28, Institute of Mathematics and Statistics, Hayward, CA, 1996, pp. 198-212] provide bounds on the distribution and on the tail for functions of dependent random vectors having fixed multivariate marginals. We correct a result stated in the above article and we give improved bounds in the case of the sum of identically distributed random vectors. Moreover, we provide the dependence structures meeting the bounds when the fixed marginals are uniformly distributed on the k-dimensional hypercube. Finally, a definition of a multivariate risk measure is given along with actuarial/financial applications. This is a joint work with Paul Embrechts, to appear in Journal of Multivariate Analysis.
Download slides of the talk [pdf/695kb]
|14:00-14:50||Dr. Riccardo Gusso
(Department of Applied Mathematics, University of Venice)
Urn-Based Credit Risk Models for Portfolios of Dependent Risks
Abstract: We present some models for portfolios of credit risks that take into account the dependence of defaults according to the rating of the involved counterparties. We show how these models can be derived from a multi-colour urn scheme and discuss the problems of calibration.
Download slides of the talk [pdf/429kb]
|14:50-15:40||Dr. Jörn Sass
(Research Group "Financial Mathematics", Johann Radon Institute for Computational and Applied Mathematics (RICAM))
Reducing the Risk of Optimal Portfolio Policies
Abstract: In 1969/1971 Merton derived in the continuous-time Black-Scholes model optimal dynamic portfolio policies using stochastic control theory. While the Black-Scholes pricing formula derived in the same model was widely accepted in practice, Merton's strategy never had such a success. In fact its performance is quite poor when applied to market data.
While the drift plays no role for pricing derivatives, it is of uttermost importance for portfolio optimization. So we might improve the performance by considering models of stock returns with a stochastic drift process. But then neither the drift nor the underlying Brownian motion can be observed from the stock prices: The investor has only partial information and his investment decisions have to be based on the observation of the stock prices only.
For the investor's objective to maximize the expected utility of the terminal wealth, optimal strategies can be computed explicitly in certain models using filtering techniques and Malliavin calculus. For logarithmic utility the fraction of wealth invested in the stocks is simply proportional to the filter for the drift. But for non-constant drift this leads to extreme short and long positions. So while it is very convenient to use continuous-time models to obtain explicit strategies, the use of these strategies is very risky, especially when trading 'only' daily.
In a continuous-time hidden Markov model for the stock returns, we compare different constraints and model reformulations, which lead to a better performance of the optimal continuous-time strategies when applied to market data: Like using risk-averse utility functions, non-constant volatility models, Lévy noise, convex constraints (e.g. no short selling), or risk constraints (e.g. bounded shortfall risk).
Download slides of the talk [pdf/154kb]
| Dr. Hansjörg Albrecher
(Department of Mathematical Sciences, University of Aarhus and Department of Mathematics A, Graz University of Technology)
Ruin Estimates for an Insurance Portfolio with Dependent Risks
Abstract: The classical stochastic model in collective risk theory to describe the surplus process of an insurance portfolio over time is based on the assumption of independence of claim sizes and claim arrival times. However, it has been recognized that such an independence assumption is often too restrictive for practical applications. We will give an overview of some recent results on the probability of ruin and related quantities in generalized models that allow for certain types of dependence.
Participation is free, and there is no official registration - nevertheless we would be happy if you write for administrative reasons a short e-mail to our secretary Sandra.Trenovatz@fam.tuwien.ac.at with your name and university or company.
Everyone is welcome, practitioners are especially encouraged to attend.