A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time

TL;DR

This paper establishes the existence of a value and equilibrium in a finite-horizon continuous-time two-player zero-sum switching game using doubly reflected BSDEs with interconnected barriers.

Contribution

It introduces a novel probabilistic verification theorem for such games, linking game value and equilibrium to solutions of doubly reflected BSDEs.

Findings

Game has a well-defined value and equilibrium

Connection between game solutions and doubly reflected BSDEs

Framework applicable to finite-horizon switching games

Abstract

In this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected BSDEs with interconnected barriers, we show that this game has a value and an equilibrium in the players' switching controls.