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 an asset whose rate of return is unknown to both players. Using filtering techniques, we first reduce the problem to a zero-sum Dynkin game on a bidimensional diffusion (X,Y). Then we characterize the existence of a Nash equilibrium in pure strategies in which each player stops at the hitting time of (X,Y) to a set with a moving boundary. A detailed description of the stopping sets for the two players is provided along with global C¹ regularity of the value function.