Maximum principle for optimal control of interacting particle system: stochastic flow model
Probability
2025-05-14 v2
Abstract
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential equation with interaction. The existence and uniqueness of the solution of this type of equation is proved. We derive the necessary condition that the optimal control should satisfy. As an application, the linear quadratic case is investigated to illustrate the main results.
Cite
@article{arxiv.2401.08075,
title = {Maximum principle for optimal control of interacting particle system: stochastic flow model},
author = {Andrey A. Dorogovtsev and Yuecai Han and Kateryna Hlyniana and Yuhang Li},
journal= {arXiv preprint arXiv:2401.08075},
year = {2025}
}