This paper studies a 2-players 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 bi-dimensional 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 moving boundary. A detailed description of the stopping sets for the two players is provided along with global C1 regularity of the value function.
Tiziano De Angelis, Fabien Gensbittel, and Stéphane Villeneuve, “A Dynkin game on assets with incomplete information on the return”, TSE Working Paper, n. 17-815, May 2017.
Mathematics of Operations Research, 2020, forthcoming