Optimal stopping with dynamic variational preferences

We consider optimal stopping problems in uncertain environments for an agent assessing utility by virtue of dynamic variational preferences as in [15] or, equivalently, assessing risk by dynamic convex risk measures as in [4]. The solutionis achieved by generalizing the approach in [20]introducing the concept of variational super martingales and an accompanying theory. To illustrate results, we consider prominent examples: dynamic entropic risk measures and a dynamic version of generalized average value at riskintroduced in [5]. -- Optimal Stopping ; Uncertainty ; Dynamic Variational Preferences ; Dynamic Convex Risk Measures ; Dynamic Penalty ; Time-Consistency ; Entropic Risk ; Average Value at Risk