Closed-loop Equilibrium for Time-Inconsistent McKean-Vlasov Controlled Problem

2020/02/17 by Hongwei Mei, Chao Zhu, Mei, Hongwei +1
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #FOS: Mathematics #Monetary Policy and Economic Impact #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.OC

paper · pdf · doi:10.48550/arxiv.2002.06952

arxiv created 2020/02/17 · openalex publication_date 2020/02/17 · arxiv updated 2020/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper deals with a class of time-inconsistent control problems for McKean-Vlasov dynamics. By solving a backward time-inconsistent Hamilton-Jacobi-Bellman (HJB for short) equation coupled with a forward distribution-dependent stochastic differential equation, we investigate the existence and uniqueness of a closed-loop equilibrium for such time-inconsistent distribution-dependent control problem. Moreover, a special case of semi-linear McKean-Vlasov dynamics with a quadratic-type cost functional is considered due to its special structure.

Citations

• Time-Inconsistent Problems for Controlled Markov Chains with Distribution-Dependent Costs: Equilibrium Solutions

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