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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 problems 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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Cite

BibTeXRIS
BibTeX
@misc{wang2026solution,
  title = {{Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay}},
  author = {Duocheng Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.26424},
  eprint = {2608.26424},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.26424},
}
RIS
TY  - UNPB
TI  - Solution to a fully coupled McKean-Vlasov forward-backward stochastic difference equation and applications to optimal control with law-delay
AU  - Duocheng Wang
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2608.26424
UR  - https://arxiv.org/abs/2608.26424
AB  - In this paper, motivated by discrete-time McKean-Vlasov optimal control problems 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.
ER  -