We will study the superhedging price (and superhedging strategies) of European and American options in a non-linear incomplete market model with default, with a particular focus on the American options case which is more involved.
We will provide a dual representation of the seller’s (superhedging) price for the American option in terms of a mixed stochastic control/stopping problem with non-linear expectations/ evaluations, and in terms of non-linear Reflected BSDEs with constraints. If time permits, we will also present a duality result for the buyer’s price in terms of a stochastic game of control and stopping with non-linear expectations/ evaluations.