Exponential Quadratic BSDEs with infinite activity Jumps

TL;DR

This paper investigates a class of backward stochastic differential equations with jumps of infinite activity, establishing existence results using exponential quadratic semimartingale techniques for equations with unbounded terminal conditions.

Contribution

It introduces a novel approach based on exponential quadratic semimartingales to prove existence of solutions for quadratic BSDEs with infinite activity jumps and unbounded terminal conditions.

Findings

Proved existence of solutions for quadratic BSDEJs with infinite activity jumps.

Extended the theory to handle unbounded terminal conditions.

Developed a forward approach using exponential quadratic semimartingales.

Abstract

In this paper, we study a Backward Stochastic Differential Equation with Jumps (BSDEJs in short) where the jumps have infinite activity. Following a forward approach based on Exponential Quadratic semimartingale, we prove the existence of solution of Quadratic BSDEJs with unbounded terminal condition and quadratic growth in z.