Optimal stopping under gg-expectation with constraints

In this paper, we study a constrained optimal stopping problem under gΓgΓ-expectation. We usegΓgΓ-expectation to evaluate the reward process. Along with the classic way of the martingale method to solve such problems, in our constrained case, the main difficulty comes from the lack of perfect continuous dependence and strict comparison property of the gΓgΓ-solution. We overcome this by additional assumptions on the reward process or convexity on gΓgΓ-expectation, and adopt a new way to get a RCLL modification of the value process by the monotonic limit theorem obtained in (Peng, 1999) [16]. We also give a short discussion about the dynamic programming principle and corresponding variational inequalities. Some examples are given in Section 3 to show our ideas and applications.