OPTIMAL STOPPING UNDER ADVERSE NONLINEAR EXPECTATION AND RELATED GAMES

• 成果类型: Article
• 署名作者: Nutz, Marcel; Zhang, Jianfeng
• 署名单位: Columbia University; University of Southern California
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1054
• 发表日期: 2015
• 页码: 2503-2534
• 关键词: g-brownian motion; stochastic calculus; part

摘要

We study the existence of optimal actions in a zero-sum game inf(tau) sup(P) E-P [X-tau] between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem inf(tau) epsilon(X-tau) for a class of sublinear expectations epsilon(.) 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.