MCKEAN-VLASOV OPTIMAL CONTROL: THE DYNAMIC PROGRAMMING PRINCIPLE

• 成果类型: Article
• 署名作者: Djete, Mao Fabrice; Possamai, Dylan; Tan, Xiaolu
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; Swiss Federal Institutes of Technology Domain; ETH Zurich; Chinese University of Hong Kong
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1548
• 发表日期: 2022
• 页码: 791-833
• 关键词: inconsistent stochastic-control; VISCOSITY SOLUTIONS; games

摘要

We study the McKean-Vlasov optimal control problem with common noise which allow the law of the control process to appear in the state dynamics under various formulations: strong and weak ones, Markovian or non-Markovian. By interpreting the controls as probability measures on an appropriate canonical space with two filtrations, we then develop the classical measurable selection, conditioning and concatenation arguments in this new context, and establish the dynamic programming principle under general conditions.