2020/06/19 by Mao Fabrice Djete, Djete, Mao Fabrice · 6 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2006.12996
openalex publication_date 2020/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the extended mean field control problem, which is a class of McKean-Vlasov stochastic control problem where the state dynamics and the reward functions depend upon the joint (conditional) distribution of the controlled state and the control process. By considering an appropriate controlled Fokker-Planck equation, we can formulate an optimization problem over a space of measure-valued processes and, under suitable assumptions, prove the equivalence between this optimization problem and the extended mean-field control problem. Moreover, with the help of this new optimization problem, we establish the associated limit theory i.e. the extended mean field control problem is the limit of a large population control problem where the interactions are achieved via the empirical distribution of state and control processes.