Explicit Solution of Infinite-Horizon Linear Backward Stochastic Volterra Integral Equations

TL;DR

This paper develops an explicit solution framework for infinite-horizon linear backward stochastic Volterra integral equations, extending finite-horizon results using advanced stochastic calculus techniques.

Contribution

It introduces a novel approach to solve infinite-horizon linear BSVIEs explicitly, including the construction of a resolvent kernel and solution formulas.

Findings

Existence and uniqueness of solutions established

Explicit formulas for solution components derived

Extension of finite-horizon theory to infinite horizon

Abstract

We study linear backward stochastic Volterra integral equations (BSVIEs) on the infinite time horizon. By introducing weighted function spaces with exponential decay, we establish existence and uniqueness of adapted M-solutions. We construct an infinite-horizon resolvent kernel and derive explicit formulas for the solution components (Y,Z,K) using a Girsanov transformation and Hida-Malliavin calculus. The results extend the finite-horizon theory of Hu and Oksendal to the infinite horizon framework.