I will talk about recent results for zero-sum games between a stopper and a singular controller. Two problems will be discussed. In the first one the controller is not allowed to exert control in all directions. In the second one, the dynamics of the underlying diffusion is degenerate. Both of these games cannot be treated with variational methods developed in [Bovo et al., MOR, 2024]. Instead, we develop approximation schemes which enable us to prove the existence of the value and of the strategy for the stopper. I will discuss the approximation procedure and the convergence of stopper’s strategies to a stopping time of a non-standard form. The talk is based on joint works with Andrea Bovo and Tiziano De Angelis.

Jan Palczewski is an Associate Professor at the School of Mathematics, University of Leeds. His research has evolved around stochastic control,optimal stopping and their applications in finance and energy. His most recent interests are focused on stochastic games,particularly, stopping games with asymmetric information.