Finite and infinite time horizon for BSDE with Poisson jumps

TL;DR

This paper investigates backward stochastic differential equations with Poisson jumps over finite and infinite horizons, establishing existence, uniqueness, and minimal solutions under various conditions.

Contribution

It introduces new existence and uniqueness results for BSDEs with jumps over both finite and infinite time horizons, including minimal solutions under linear growth.

Findings

Existence of minimal solutions under linear growth conditions

Uniqueness of solutions with uniformly continuous generators

Applicability to both finite and infinite time horizons

Abstract

This paper is devoted to solving a real valued backward stochastic differential equation with jumps where the time horizon may be finite or infinite. Under linear growth generator, we prove existence of a minimal solution. Using a comparison theorem we show existence and uniqueness of solution to such equations when the generator is uniformly continuous and satisfies a weakly monotonic condition.