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Closed-loop Equilibrium for Time-Inconsistent McKean-Vlasov Controlled Problem (2002.06952v1)

Published 17 Feb 2020 in math.OC

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.