Optimal Stopping Under Uncertainty in Drift and Jump Intensity

• 成果类型: Article
• 署名作者: Kraetschmer, Volker; Ladkau, Marcel; Laeven, Roger J. A.; Schoenmakers, John G. M.; Stadjed, Mitja
• 署名单位: University of Duisburg Essen; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Amsterdam; Ulm University; Ulm University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2017.0899
• 发表日期: 2018
• 页码: 1177-1209
• 关键词: coherent measures; expected utility; exact simulation; nonlinear expectations; penalty-functions; American options; convex measures; Risk measures; ambiguity; MODEL

摘要

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.