ON VISCOSITY SOLUTIONS OF PATH DEPENDENT PDES

• 成果类型: Article
• 署名作者: Ekren, Ibrahim; Keller, Christian; Touzi, Nizar; Zhang, Jianfeng
• 署名单位: University of Southern California; Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP788
• 发表日期: 2014
• 页码: 204-236
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; nonlinear 2nd-order equations; infinite dimensions; parabolic PDEs; backward sdes

摘要

In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward SDEs, and thus extends the well-known nonlinear Feynman-Kac formula to non-Markovian case. We shall prove the existence, uniqueness, stability and comparison principle for the viscosity solutions. The key ingredient of our approach is a functional Ito calculus recently introduced by Dupire [Functional Ito calculus (2009) Preprint].