Maximum principle for optimal control of interacting particle system: stochastic flow model

Andrey A. Dorogovtsev, Yuecai Han, Kateryna Hlyniana, Yuhang Li

Published 2024-01-16Version 1

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.