Anticipating backward stochastic Volterra integral equations

TL;DR

This paper introduces anticipating backward stochastic Volterra integral equations (BSVIEs), analyzing their properties and establishing existence, uniqueness, and comparison theorems for solutions involving future and present values.

Contribution

The paper presents the first study of anticipating BSVIEs, extending classical BSVIE theory to include future-dependent generators and proving fundamental solution properties.

Findings

Existence and uniqueness of solutions for anticipating BSVIEs

Comparison theorem for solutions of anticipating BSVIEs

Extension of BSVIE theory to future-dependent generators

Abstract

We introduce and study a new type of integral equations called anticipating backward stochastic Volterra integral equations (anticipating BSVIEs). In these equations the generator involves not only the present values but also the future values of the solutions. We obtain the existence and uniqueness theorem and a comparison theorem for the solutions to these anticipating BSVIEs.