Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

摘要

The present paper considers a stochastic optimal control problem, in whichthe cost function is defined through a backward stochastic differentialequation with infinite horizon driven by G-Brownian motion. Then we study theregularities of the value function and establish the dynamic programmingprinciple. Moreover, we prove that the value function is the uniquenessviscosity solution of the related HJBI equation.