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Author: Schoenmakers, John G. M. × Subject: Optimal stopping ×

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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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    Solving optimal stopping problems via randomization and empirical dual optimization
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Belomestny, Denis; Bender, Christian; Schoenmakers, John G. M.
    In this paper we consider optimal stopping problems in their dual form. In this way we reformulate the optimal stopping problem as a problem of stochastic average approximation (SAA) which can be solved via linear programming. By randomizing the initial value of the underlying process, we enforce solutions with zero variance while preserving the linear programming structure of the problem. A careful analysis of the randomized SAA algorithm shows that it enjoys favorable properties such as faster convergence rates and reduced complexity as compared to the non randomized procedure. We illustrate the performance of our algorithm on several benchmark examples.