Infinite Horizon Multi-Dimensional BSDE with Oblique Reflection and Switching Problem

TL;DR

This paper investigates a complex system of multi-dimensional reflected backward stochastic differential equations with oblique reflections over an infinite horizon, focusing on switching problems, and establishes existence and uniqueness of solutions using advanced mathematical techniques.

Contribution

It introduces a novel approach combining penalization, verification, and contraction methods to prove existence and uniqueness of solutions for infinite horizon multi-dimensional RBSDEs with oblique reflection.

Findings

Existence and uniqueness of solutions established

Method successfully handles infinite horizon and oblique reflection complexities

Provides a mathematical foundation for switching problems in stochastic control

Abstract

This paper studies a system of multi-dimensional reflected backward stochastic differential equations with oblique reflections (RBSDEs for short) in infinite horizon associated to switching problems. The existence and uniqueness of the adapted solution is obtained by using a method based oa combination of penalization, verification method and contraction property.