Optimal Stopping Under Uncertainty in Drift and Jump Intensity

Volker Krätschmer (), Marcel Ladkau (), Roger Laeven, John G. M. Schoenmakers () and Mitja Stadje ()
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Volker Krätschmer: Faculty of Mathematics, University of Duisburg-Essen, D-45127 Essen, Germany
Marcel Ladkau: Weierstrass Institute Berlin, Stochastic Algorithms and Nonparametric Statistics, D-10117 Berlin, Germany
John G. M. Schoenmakers: Weierstrass Institute Berlin, Stochastic Algorithms and Nonparametric Statistics, D-10117 Berlin, Germany
Mitja Stadje: Institute of Insurance Science and Institute of Financial Mathematics, Faculty of Mathematics and Economics, Ulm University, D-89069 Ulm, Germany

Mathematics of Operations Research, 2018, vol. 43, issue 4, 1177-1209

Abstract: This paper studies the optimal stopping problem in the presence of model uncertainty (ambiguity). We develop a numerically implementable method to 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 also provide asymptotically optimal exercise rules. We analyze the limiting 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.

Keywords: optimal stopping; model uncertainty; robustness; convex risk measures; ambiguity aversion; duality; BSDEs; Monte Carlo simulation; regression; relative entropy (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:43:y:2018:i:4:p:1177-1209

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