Two-stage stochastic optimal control problem under G-expectation

Abstract

This paper is dedicated to a kind of stochastic two-stage optimal control problem (TSOC) under $G$-expectation. The system’s state switches at a given time point and the cost function involves stages on two time horizons in order to achieve two-stage management. A motivation of Problem TSOC is presented. A novel sufficient optimality condition (SOCD) is given via a sequence of adjoint processes coupled by jump boundary conditions under a maximal reference probability, which is more concise and applicable compared to previous results. Analytical results in two-stage linear-quadratic (TSLQ) case are presented, where a feedback optimal control (OC) is designed and a maximal reference probability is determined. Moreover, some interesting impacts of probability uncertainty and additional cost term to Problem TSLQ are analyzed, which are meaningful to practical risk management. Numerical simulations are presented to illustrate our theoretical results.