RANDOMIZED AND BACKWARD SDE REPRESENTATION FOR OPTIMAL CONTROL OF NON-MARKOVIAN SDES

• 成果类型: Article
• 署名作者: Fuhrman, Marco; Huyen Pham
• 署名单位: Polytechnic University of Milan; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1045
• 发表日期: 2015
• 页码: 2134-2167
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; VISCOSITY SOLUTIONS

摘要

We study optimal stochastic control problems for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients and gain functionals are path-dependent, and importantly we do not make any ellipticity assumptions on the SDE. We develop a control randomization approach and prove that the value function can be reformulated under a family of dominated measures on an enlarged filtered probability space. This value function is then characterized by a backward SDE with nonpositive jumps under a single probability measure, which can be viewed as a path-dependent version of the Hamilton Jacobi Bellman equation, and an extension to G-expectation.