A Dynkin Game on Assets with Incomplete Information on the Return

This paper studies a two-player zero-sum Dynkin game arising from pricing an option on asset whose rate of return is unknown to both players. Using filtering techniques, we first reduce the problem bidimensional diffusion (X,Y). Then characterize existence Nash equilibrium in pure strategies which each player stops at hitting time (X,Y) set with moving boundary. A detailed description stopping sets for two players provided along global C 1 regularity value function.