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Author: Krätschmer, Volker ×

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    Central limit theorems for law-invariant coherent risk measures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Belomestny, Denis; Krätschmer, Volker
    In this paper we study the asymptotic properties of the canonical plug-in estimates for law-invariant coherent risk measures. Under rather mild conditions not relying on the explicit representation of the risk measure under consideration, we first prove a central limit theorem for independent identically distributed data and then extend it to the case of weakly dependent ones. Finally, a number of illustrating examples is presented.
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    A microeconomic explanation of the epk paradox
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Härdle, Wolfgang Karl; Krätschmer, Volker; Rouslan, Moro
    Supported by some recent investigations the empirical pricing kernel paradox might be viewed as a stylized fact. In ChabiYo et al. (2008) simulation studies have been presented which suggest that this paradox might be caused by regime switching of stock prices in financial markets. Alternatively, we want to emphasize a microeconomic view. Based on an economic model with state dependent utilities for the financial investors we succeed in explaining the paradox by changes of risk attitudes. Theoretically, the change behaviour is compressed in the pricing kernels. As a starting point for empirical insights we shall develop and investigate inverse problems in terms of data fits for estimated basic values of the pricing kernel.
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    Representations for optimal stopping under dynamic monetary utility functionals
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Krätschmer, Volker; Schoenmakers, John
    In this paper we consider the optimal stopping problem for general dynamic monetary utility functionals. Sufficient conditions for the Bellman principle and the existence of optimal stopping times are provided. Particular attention is payed to representations which allow for a numerical treatment in real situations. To this aim, generalizations of standard evaluation methods like policy iteration, dual and consumption based approaches are developed in the context of general dynamic monetary utility functionals. As a result, it turns out that the possibility of a particular generalization depends on specific properties of the utility functional under consideration.
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    Sensitivity of risk measures with respect to the normal approximation of total claim distributions
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Krätschmer, Volker; Zähle, Henryk
    A simple and commonly used method to approximate the total claim distribution of a (possible weakly dependent) insurance collective is the normal approximation. In this article, we investigate the error made when the normal approximation is plugged in a fairly general distribution-invariant risk measure. We focus on the rate of the convergence of the error relative to the number of clients, we specify the relative error's asymptotic distribution, and we illustrate our results by means of a numerical example. Regarding the risk measure, we take into account distortion risk measures as well as distribution-invariant coherent risk measures.
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    Robust optimal stopping
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Krätschmer, Volker; Ladkau, Marcel; Laeven, Roger J.A.; Schoenmakers, John G.M.; Stadje, Mitja
    This paper studies the optimal stopping problem in the presence of model uncertainty (ambiguity). We develop a method to practically solve this problem in a general setting, allowing for general time-consistent ambiguity averse preferences and general payoff processes driven by jump-diffusions. Our method consists of three steps. First, we construct a suitable Doob martingale associated with the solution to the optimal stopping problem using backward stochastic calculus. Second, we employ this martingale to construct an approximated upper bound to the solution using duality. Third, we introduce backward-forward simulation to obtain a genuine upper bound to the solution, which converges to the true solution asymptotically. We analyze the asymptotic behavior and convergence properties of our method. We illustrate the generality and applicability of our method and the potentially significant impact of ambiguity to optimal stopping in a few examples.