Generalized Dynkin games and game options in an imperfect market with default

Speaker(s): 
Roxana Dumitrescu (HU Berlin)
Date: 
Thursday, December 3, 2015 - 4:15pm
Location: 
HU Berlin, Rudower Chaussee 25, Room 1.115

In the first part of the talk, we introduce a generalized Dynkin game problem with non linear conditional expectation induced by a Backward Stochastic Differential Equation (BSDE) with jumps. Under Mokobodski's condition, we establish the existence of a value function for this game. This value can be characterized via a doubly reflected BSDE. Using this characterization, we provide some new results on these equations, such as comparison theorems and a priori estimates. When the obstacles are left upper semicontinuous along stopping times, we prove the existence of a saddle point. We also study a generalized mixed game problem when the players have two actions: continuous control and stopping.
In the second part of the talk, we study the 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 on the market taken into account via the nonlinearity of the wealth dynamics. 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. 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 with M.C. Quenez and A. Sulem).