ZERO-SUM PATH-DEPENDENT STOCHASTIC DIFFERENTIAL GAMES IN WEAK FORMULATION

• 成果类型: Article
• 署名作者: Possamai, Dylan; Touzi, Nizar; Zhang, Jianfeng
• 署名单位: Columbia University; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; University of Southern California
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/19-AAP1533
• 发表日期: 2020
• 页码: 1415-1457
• 关键词: dynamic-programming principle; VISCOSITY SOLUTIONS; perrons method; Representation theorem; Contingent claims; EXISTENCE; strategies; EQUATIONS

摘要

We consider zero-sum stochastic differential games with possibly path-dependent volatility controls. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback type. In particular, we do not require the controls to be simple, which has fundamental importance for the possible existence of saddle-points. Under some restrictions, needed for the a priori regularity of the upper and lower value functions of the game, we show that the game value exists when both the appropriate path-dependent Isaacs condition, and the uniqueness of viscosity solutions of the corresponding path-dependent Isaacs-HJB equation hold. We also provide a general verification argument and a characterisation of saddle-points by means of an appropriate notion of second-order backward SDE.