The stochastic maximum principle in singular optimal control with recursive utilities

Abstract

In this paper, we consider stochastic recursive optimal control problem, in which the control variable has two components with the first absolutely continuous and the second singular. The control domain of the first component needs not to be convex. By using a spike variation on the absolutely continuous part of the control and a convex perturbation on the singular one respectively, we obtain a stochastic maximum principle of the optimal control. Also, we give the relationship of the backward variational equation, the adjoint equation and forward variational equation.