Backward stochastic viability property with jumps and applications to the comparison theorem for multidimensional BSDEs with jumps

TL;DR

This paper investigates conditions ensuring solutions of backward stochastic differential equations with jumps stay within certain constraints, and applies these results to establish a comparison theorem for multidimensional BSDEs with jumps.

Contribution

It introduces viability conditions for BSDEs with jumps and applies them to prove a comparison theorem in the multidimensional jump setting.

Findings

Established viability conditions for BSDEs with jumps

Proved a comparison theorem for multidimensional BSDEs with jumps

Enhanced understanding of constrained stochastic processes

Abstract

In this paper, we study conditions under which the solutions of a backward stochastic differential equation with jump remains in a given set of constrains. This property is the so-called "viability property". As an application, we study the comparison theorem for multidimensional BSDEs with jumps.