Zero-sum Switching Game, Systems of Reflected Backward SDEs and Parabolic PDEs with bilateral interconnected obstacles

TL;DR

This paper establishes the connection between a zero-sum switching game, systems of reflected backward stochastic differential equations, and parabolic PDEs with bilateral interconnected obstacles, proving existence, uniqueness, and the existence of a game value.

Contribution

It introduces a novel framework linking zero-sum switching games with systems of RBSDEs and PDEs with interconnected obstacles, proving their well-posedness and the existence of a game value.

Findings

Unique solutions for systems of RBSDEs and PDEs with bilateral interconnected obstacles.

The zero-sum switching game has a well-defined value.

Verification theorems connect the game to the systems of equations.

Abstract

In this paper we study a zero-sum switching game and its verification theorems expressed in terms of either a system of Reflected Backward Stochastic Differential Equations (RBSDEs in short) with bilateral interconnected obstacles or a system of parabolic partial differential equations (PDEs in short) with bilateral interconnected obstacles as well. We show that each one of the systems has a unique solution. Then we show that the game has a value.