Explicit solution for backward stochastic Volterra integral equations with linear time delayed generators

TL;DR

This paper provides an explicit solution for backward stochastic Volterra integral equations with linear time-delayed generators, expressing the processes explicitly using kernels and derivatives.

Contribution

It introduces an explicit solution method for a class of backward stochastic Volterra integral equations with linear time delays.

Findings

Explicit kernel expression for process Y.

Representation of process Z via Hida-Malliavin derivatives.

Solution facilitates analysis of delayed stochastic systems.

Abstract

This note aims to give an explicit solution for backward stochastic Volterra integral equations with linear time delayed generators. The process $Y$ is expressed by an integral whose kernel is explicitly given. The processes $Z$ is expressed by Hida-Malliavin derivatives involving $Y$.