We study pricing and superhedging strategies for game options in an imperfect market with default. We extend the results obtained by Kifer  Kifer in the case of a perfect market model to the case of imperfections on 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{\em  {  coincides with the value function of a corresponding {\em generalized} Dynkin game expressed in terms of the g-evaluation , recently introduced in DQS2 . 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 {\em 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 . This study is introduced by the analysis of the simpler case of American options .
We study pricing and superhedging strategies for game options in an imperfect market with default. We extend the results obtained by Kifer in Kifer in the case of a perfect market model to the case of an imperfect market with default, when the imperfections are taken into account via the nonlinearity of the wealth dynamics. We introduce the{\em seller's price of the game option as the infimum of the initial wealths which allow the seller to be superhedged. We{prove that this price coincides with the value function of an associated {\em generalized} Dynkin game , recently introduced in DQS2 , expressed with a nonlinear expectation induced by a nonlinear BSDE with default jump. We moreover study the existence of superhedging strategies. We then address the case of ambiguity on the model, - for example ambiguity on the default probability - and characterize the robust seller's price of a game option as the value function of a {\em mixed generalized} Dynkin game. We study the existence of a cancellation time and a trading strategy which allow the seller to be super-hedged, whatever the model is .
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