On Peng's type maximum principle for optimal control of mean-field stochastic differential equations with jump processes

Abstract

In this paper we investigate the Peng's type optimal control problems for stochastic differential equations of mean-field type with jump processes. The coefficients of the system contain not only the state process but also its marginal distribution through their expected values. We assume that the control set is a general open set that is not necessary convex. The control variable is allowed to enter into both diffusion and jump terms. We extend the maximum principle of Buckdahn et al. (2011) to jump case.