Stochastic maximum principle for generalized mean-field delay control problem

Abstract

In this paper, we first give the existence and uniqueness theorems for generalized mean-filed delay stochastic differential equations (GMFDSDEs) and mean-field anticipated backward stochastic differential equations (MFABSDEs). Then we study the stochastic maximum principle for generalized mean-filed delay control problem. Since the state is distribution-depending, we define the adjoint equation as a MFABSDE, in which, all the derivatives of coefficients are in Fréchet sense. We deduce the stochastic maximum principle, and also obtain, under some additional assumptions, a sufficient condition for the optimality of the control.

29 pages, 0 figures. arXiv admin note: text overlap with arXiv:1704.08002