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Author: Krätschmer, Volker × Subject: duality ×

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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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    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.