Some Properties of Reflected Backward Stochastic Differential Equations for a Finite State Markov Chain Model

TL;DR

This paper investigates properties of reflected backward stochastic differential equations driven by a finite state Markov chain, including estimates, dependence on parameters, and comparison results, advancing the understanding of such equations in stochastic modeling.

Contribution

It provides new estimates, continuity properties, and comparison theorems for RBSDEs driven by Markov chains, extending existing theory to this setting.

Findings

Derived solution estimates for RBSDEs

Established continuous dependence on parameters

Proved comparison results for solutions

Abstract

In this paper, we provide an estimate for the solutions of reflected backward stochastic differential equations (RBSDEs) driven by a Markov chain, derive a continuous dependence property for their solutions with respect to the parameters of the equations, and show similar properties for solutions of backward stochastic differential equations (BSDEs). We finally establish a comparison result for the solutions of RBSDEs driven by a Markov chain.