Linear Volterra backward stochastic differential equations

TL;DR

This paper provides explicit solutions for linear backward stochastic Volterra integral equations driven by Brownian motion and Poisson measures, expressing solutions through kernels and derivatives, advancing understanding of such equations.

Contribution

It introduces explicit solution formulas for linear BSVIEs, linking solutions to kernels and Hida-Malliavin derivatives, which was not previously established.

Findings

Explicit solution triplet (Y, Z, K) derived

Solutions expressed via integral kernels and derivatives

Advances analytical understanding of linear BSVIEs

Abstract

We present an explicit solution triplet $(Y, Z, K)$ to the backward stochastic Volterra integral equation (BSVIE) of linear type, driven by a Brownian motion and a compensated Poisson random measure. The process $Y$ is expressed by an integral whose kernel is explicitly given. The processes $Z$ and $K$ are expressed by Hida-Malliavin derivatives involving $Y$.