International Journal of Control, Vol.93, No.4, 953-970, 2020
Optimal control of mean-field backward doubly stochastic systems driven by Ito-Levy processes
In this paper, we introduce a new class of backward doubly stochastic differential equations (in short BDSDE) called mean-field backward doubly stochastic differential equations (in short MFBDSDE) driven by Ito-Levy processes and study the partial information optimal control problems for backward doubly stochastic systems driven by Ito-Levy processes of mean-field type, in which the coefficients depend on not only the solution processes but also their expected values. First, using the method of contraction mapping, we prove the existence and uniqueness of the solutions to this kind of MFBDSDE. Then, by the method of convex variation and duality technique, we establish a sufficient and necessary stochastic maximum principle for the stochastic system. Finally, we illustrate our theoretical results by an application to a stochastic linear quadratic optimal control problem of a mean-field backward doubly stochastic system driven by Ito-Levy processes.