Before revision:  Moreover, exploiting the theory of sublinear expectations, we define a nonlinear Snell envelope Y and prove that the first hitting time \inf{t:\, Y_t=X_t is an optimal stopping time.
After revision:  Moreover, exploiting the theory of sublinear expectations, we define a nonlinear Snell envelope Y and prove that the first hitting time \inf\{t:Y_t=X_t\ is an optimal stopping time.