Article

A Dynkin game on assets with incomplete information on the return

Tiziano De Angelis, Fabien Gensbittel, and Stéphane Villeneuve

Abstract

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.

Replaces

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.

Reference

Tiziano De Angelis, Fabien Gensbittel, and Stéphane Villeneuve, A Dynkin game on assets with incomplete information on the return, Mathematics of Operations Research, 2020, forthcoming.

Published in

Mathematics of Operations Research, 2020, forthcoming