Stochastic Volterra integral equations with jumps and non-Lipschitz coefficients

TL;DR

This paper studies the existence and uniqueness of solutions to stochastic Volterra integral equations with jumps, driven by Brownian motion and Poisson measures, under non-Lipschitz conditions, using successive approximation methods.

Contribution

It introduces a novel approach to establish solution existence and uniqueness for SVIEs with jumps under non-Lipschitz conditions, expanding theoretical understanding.

Findings

Proves existence of solutions under non-Lipschitz conditions.

Establishes uniqueness of solutions for SVIEs with jumps.

Extends classical results to more general conditions.

Abstract

Stochastic Volterra integral equations with jumps (SVIEs) have become very common and widely used in numerous branches of science, due to their connections with mathematical finance, biology, engineering and so on. In this paper, we apply the successive approximation method to investigate the existence and uniqueness of solutions to the SVIEs driven by Brownian motion and compensated Poisson random measure under non-Lipschitz condition.