Stochastic differential switching game in infinite horizon

TL;DR

This paper analyzes a zero-sum stochastic differential switching game over an infinite horizon, establishing the existence of the game's value, characterizing it via viscosity solutions, and providing optimal strategies with numerical examples.

Contribution

It introduces a novel analysis of infinite horizon switching games, proving value existence, and characterizing it through quasi-variational inequalities with a verification theorem.

Findings

Existence of the game's value proved.

Characterization of the value as a viscosity solution.

Numerical examples illustrating two-regime scenarios.

Abstract

We study a zero-sum stochastic differential switching game in infinite horizon. We prove the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities with bilateral obstacles. We also obtain a verification theorem which provides an optimal strategy of the game. Finally, some numerical examples with two regimes are given.