The near-optimal maximum principle of impulse control for stochastic recursive system

Here, we discuss the near-optimality for a class of stochastic impulse control problems. The state process in our problem is given by forward-backward stochastic differential equations (FBSDEs) with two control components involved: the regular and impulse control. More specially, the impulse control is defined on a sequence of prescribed stopping times. A recursive cost functional is introduced and the maximum principle for its near-optimality (both necessary and sufficient conditions) is derived with the help of Ekeland's principle and variational analysis. For illustration, one concrete example is studied with our maximum principle and the corresponding near-optimal control is characterized.