# A Dynkin game on assets with incomplete information on the return

## TL;DR

This paper analyzes a zero-sum Dynkin game for option pricing with incomplete return information, using filtering to reduce the problem and characterizing Nash equilibria with moving boundary stopping strategies.

## Contribution

It introduces a novel approach to model and solve a Dynkin game under incomplete information by reducing it to a bi-dimensional diffusion and characterizing pure strategy equilibria.

## Key findings

- Existence of Nash equilibrium in pure strategies with hitting times
- Characterization of stopping sets with moving boundaries
- Global $C^1$ regularity of the value function

## 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 $C^1$ regularity of the value function.