Backward stochastic differential equations with regime-switching and sublinear expectations

TL;DR

This paper develops backward stochastic differential equations driven by Brownian motion and Markov chains, establishing existence, uniqueness, and comparison theorems, and characterizes sublinear expectations for pricing in regime-switching models.

Contribution

It introduces a new class of BSDEs with regime-switching and characterizes sublinear expectations as their solutions, advancing mathematical tools for financial modeling.

Findings

Proved existence and uniqueness of solutions for BSDEs with regime-switching.

Derived a comparison theorem for these BSDEs.

Represented bid and ask prices using sublinear expectations.

Abstract

This paper introduces a backward stochastic differential equation driven by both Brownian motion and a Markov chain (BSDEBM). Regime-switching is also incorporated through its driver. The existence and uniqueness of the solution of the BSDEBM are proved. A comparison theorem is also derived. Filtration consistent sublinear expectations are defined and characterized as solutions to the BSDEBM. The bid and ask prices are then represented using sublinear expectations.