The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options

TL;DR

This paper investigates nonzero-sum Dynkin games in continuous time, establishing the existence of Nash equilibria for general stochastic processes and applying the results to pricing American game options via utility maximization.

Contribution

It proves the existence of Nash equilibria in continuous-time nonzero-sum Dynkin games and applies this to the valuation of American game options.

Findings

Existence of Nash equilibrium points for general stochastic processes.

Application to pricing American game contingent claims.

Utility maximization approach used for valuation.

Abstract

In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximization approach.