Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay

Duocheng Wang

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arXiv · 2608.26424

Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay

Duocheng Wang

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Abstract

In this paper, motivated by discrete-time McKean-Vlasov optimal control problem with law-delay, a class of forward-backward stochastic difference equations is investigated. The main difficulties come from the absence of Ito's formula in the discrete-time setting, as well as the fully coupled structure in which the coefficients depend on both law-delayed and law-anticipated terms. Under suitable monotonicity conditions, the existence and uniqueness of solutions are established. Furthermore, a new monotonicity condition is introduced to address the associated optimal control problem. As an application, the unique optimal control for linear quadratic systems with law-delay is derived.

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Duocheng Wang. 2026-08-26. Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay. https://arxiv.org/abs/2608.26424

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