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    Robust multiple stopping -- A path-wise duality approach
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Laeven, Roger J. A.; Schoenmakers, John G. M.; Schweizer, Nikolaus F. F.; Stadje, Mitja
    In this paper we develop a solution method for general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model uncertainty, and for general reward processes driven by multi-dimensional jump-diffusions. Our approach relies on first establishing robust martingale dual representation results for the multiple stopping problem which satisfy appealing path-wise optimality (almost sure) properties. Next, we exploit these theoretical results to develop upper and lower bounds which, as we formally show, not only converge to the true solution asymptotically, but also constitute genuine upper and lower bounds. We illustrate the applicability of our general approach in a few examples and analyze the impact of model uncertainty on optimal multiple stopping strategies.
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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.