Recent developments in the theory of stochastic control and optimal stopping with nonlinear expectations

In this talk, we present recent developments in the theory of control and optimal stopping with nonlinear expectations, as well as their applications in finance. We first introduce an optimal stopping game with nonlinear... [ view full abstract ]

In this talk, we present recent developments in the theory of control and optimal stopping with nonlinear expectations, as well as their applications in finance. We first introduce an optimal stopping game with nonlinear expectations (Generalized Dynkin Game) in a non-Markovian framework and study its links with nonlinear doubly reflected BSDEs. These results are applied to the nonlinear pricing of game options. Some additional results are given in the case of nonlinear pricing of American options in incomplete markets with default. In the second part, we present a new mixed generalized Dynkin game/stochastic control with-expectation in a Markovian framework.