Stochastic Maximum Principle for McKean-Vlasov Control with Discrete Path Dependence
Abstract
We study a class of McKean-Vlasov control problems with discrete path dependence. The coefficients and cost functional may depend on finitely many past values of the controlled state, observed at fixed deterministic times, and on their joint law. We establish well-posedness of the controlled state equation and derive necessary and sufficient optimality conditions through a stochastic Pontryagin maximum principle. The adjoint process is characterized by a backward stochastic differential equation with jumps at fixed observation times. Each jump represents the conditional sensitivity of future costs with respect to the corresponding observed state and its distribution. In the linear-quadratic case, we prove global solvability of the resulting forward-backward system by combining a continuation argument with a mean-field Riccati reduction. We finally discuss an application to time-series generation, where the terminal cost is given by a kernel-based discrepancy between the law of the sampled path and a target path distribution.
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BibTeX
@misc{hafsi2026stochastic,
title = {{Stochastic Maximum Principle for McKean-Vlasov Control with Discrete Path Dependence}},
author = {Yadh Hafsi and Samy Mekkaoui and Huyên Pham},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04588},
eprint = {2609.04588},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04588},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stochastic Maximum Principle for McKean-Vlasov Control with Discrete Path Dependence
AU - Yadh Hafsi
AU - Samy Mekkaoui
AU - Huyên Pham
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.04588
UR - https://arxiv.org/abs/2609.04588
AB - We study a class of McKean-Vlasov control problems with discrete path dependence. The coefficients and cost functional may depend on finitely many past values of the controlled state, observed at fixed deterministic times, and on their joint law. We establish well-posedness of the controlled state equation and derive necessary and sufficient optimality conditions through a stochastic Pontryagin maximum principle. The adjoint process is characterized by a backward stochastic differential equation with jumps at fixed observation times. Each jump represents the conditional sensitivity of future costs with respect to the corresponding observed state and its distribution. In the linear-quadratic case, we prove global solvability of the resulting forward-backward system by combining a continuation argument with a mean-field Riccati reduction. We finally discuss an application to time-series generation, where the terminal cost is given by a kernel-based discrepancy between the law of the sampled path and a target path distribution.
ER -