Roxana Dumitrescu: Game options in an imperfect market with default
Roxana Dumitrescu (King’s College, London) gives a lecture with the title: Game options in an imperfect market with default
We study pricing and superhedging strategies for game options in an imperfect market with default. We extend the results obtained by Kifer in the case of a perfect market model to the case of imperfections in the market taken into account via the nonlinearity of the wealth dynamics. In this framework, the pricing system is expressed as a nonlinear g-expectation/evaluation induced by a nonlinear BSDE with jump. We prove that the superhedging price of a game option coincides with the value function of a corresponding generalized Dynkin game expressed in terms of the g-evaluation, recently introduced by Dumitrescu,Quenez and Sulem. We then address the case of ambiguity on the model, - for example an ambiguity on the default probability - and characterize the superhedging price of a game option as the value function of a mixed generalized Dynkin game. We prove the existence of a cancellation time and a trading strategy for the seller which allow him/her to be super-hedged, whatever the model is (joint work with M.C.Quenez and A.Sulem).