STOCHASTIC TARGET GAMES WITH CONTROLLED LOSS

• 成果类型: Article
• 署名作者: Ouchard, Bruno B.; Moreau, Ludovic; Nutz, Marcel
• 署名单位: Universite PSL; Universite Paris-Dauphine; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP938
• 发表日期: 2014
• 页码: 899-934
• 关键词: g-brownian motion; VISCOSITY SOLUTIONS; differential-equations; g-expectation; uncertainty; calculus

摘要

We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscosity solutions. As an example, we consider a problem of partial hedging under Knightian uncertainty.