A general characterization of the stochastic optimal combined control of mean field stochastic systems with application

Abstract

In this paper a general characterization of the optimal stochastic combined control for mean-field jump-systems is derived by applying mixed convex-spike perturbation method. The diffusion coefficient depends on the continuous control variable and the control domain is not necessary convex. In our combined mean-field control problem we discuss two classes of jumps for the state processes the inaccessible jumps which caused by Poisson martingale measure and the predictable ones which caused by the singularity of the control variable. Markowitz’s mean–variance portfolio selection problem with intervention control is discussed. © 2020 Elsevier B.V. All rights reserved.