Stochastic optimal control of McKean-Vlasov equations with anticipating law

TL;DR

This paper extends Pontryagin's stochastic maximum principle to controlled McKean-Vlasov equations where the law depends on future states, introducing new delayed backward equations with implicit terminal conditions.

Contribution

It introduces a novel stochastic maximum principle for McKean-Vlasov equations with anticipative law dependence, including the analysis of associated delayed backward equations.

Findings

Established a new maximum principle for anticipative McKean-Vlasov control.

Derived and analyzed delayed backward equations with implicit terminal conditions.

Provided theoretical foundations for future applications in stochastic control with anticipative laws.

Abstract

In this paper, we generalise Pontryagin's stochastic maximum principle to controlled McKean-Vlasov equations with anticipating law. The associated new type of delayed backward equations with implicit terminal condition is studied.