A Dynkin game on assets with incomplete information on the return

2017/05/20 by De Angelis, Tiziano, Gensbittel, Fabien, Villeneuve, Stéphane
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.1705.07352

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.

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