Maximum Principle for Stochastic Recursive Optimal Control Problem under Model Uncertainty

Abstract

In this paper, we consider a stochastic recursive optimal control problem under model uncertainty. In this framework, the cost function is described by solutions of a family of backward stochastic differential equations with uncertainty parameter $\theta$, which is used to represent different market conditions. With the help of linearization techniques and weak convergence methods, we derive the corresponding stochastic maximum principle. Moreover, a linear quadratic robust control problem is also studied.