Solving finite time horizon Dynkin games by optimal switching

TL;DR

This paper establishes the existence of saddle points in finite-horizon Dynkin games using optimal switching theory, providing conditions for value continuity and demonstrating numerical applications in financial options.

Contribution

It introduces a novel approach connecting optimal switching problems with Dynkin games and derives conditions for value continuity in finite-horizon settings.

Findings

Existence of saddle points in finite-horizon Dynkin games.

Continuity of the game's value with respect to the time horizon.

Numerical demonstration in Black-Scholes market for options.

Abstract

This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent results on norm estimates for doubly reflected backward stochastic differential equations. This theory is then demonstrated numerically for the special cases of cancellable call and put options in a Black-Scholes market.