Optimal stopping under adverse nonlinear expectation and related games

Marcel Nutz and Jianfeng Zhang

Papers from arXiv.org

Abstract: We study the existence of optimal actions in a zero-sum game $\inf_{\tau}\sup_PE^P[X_{\tau}]$ between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem $\inf_{\tau}\mathcal{E}(X_{\tau})$ for a class of sublinear expectations $\mathcal{E}(\cdot)$ such as the $G$-expectation. We show that the game has a value. Moreover, exploiting the theory of sublinear expectations, we define a nonlinear Snell envelope $Y$ and prove that the first hitting time $\inf\{t:Y_t=X_t\}$ is an optimal stopping time. The existence of a saddle point is shown under a compactness condition. Finally, the results are applied to the subhedging of American options under volatility uncertainty.

Date: 2012-12, Revised 2015-09
New Economics Papers: this item is included in nep-gth and nep-mic
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Citations: View citations in EconPapers (32)

Published in Annals of Applied Probability 2015, Vol. 25, No. 5, 2503-2534

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1212.2140

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