General mean-field stochastic linear quadratic control problem driven by Lévy processes with random coefficients

2025/03/18 by Tang, Yanyan, Xiong, Jie
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2503.13835

Abstract

This paper studies a stochastic mean-field linear-quadratic optimal control problem with random coefficients. The state equation is a general linear stochastic differential equation with mean-field terms \EE X(t) and \EE u(t) of the state and the control processes and is driven by a Brownian motion and a Poisson random measure. By the coupled system of Riccati equations, an explicit expressions for the optimal state feedback control is obtained. As a by-product, the non-homogeneous stochastic linear-quadratic control problem with random coefficients and Lévy driving noises is also studied.

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