Reflected Backward Stochastic Volterra Integral Equations and related time-inconsistent optimal stopping problems

TL;DR

This paper investigates reflected backward stochastic Volterra integral equations driven by Brownian motion, establishing existence, uniqueness, and comparison results, and connects these solutions to time-inconsistent optimal stopping problems with derived strategies.

Contribution

It introduces a novel analysis of reflected backward stochastic Volterra integral equations and links them to time-inconsistent optimal stopping problems, providing existence, uniqueness, and optimal strategies.

Findings

Proved existence and uniqueness of solutions.

Established a comparison theorem.

Derived optimal strategies for related stopping problems.

Abstract

We study solutions of a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We prove existence and uniqueness by a fixed point argument and we derive a comparison result. Moreover, we show how the solution of our problem is related to a time-inconsistent optimal stopping problem and derive an optimal strategy.