We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the “stopper”) who chooses the termination time of the game, and an agent (the “controller,” or “nature”) who selects the probability measure.
Erhan Bayraktar. Ioannis Karatzas. Song Yao. "Optimal stopping for dynamic convex risk measures." Illinois J. Math. 54 (3) 1025 - 1067, Fall; 2010. https://doi.org/10.1215/ijm/1336049984