# Lp solutions of backward stochastic Volterra integral equations

## TL;DR

This paper establishes the existence and uniqueness of solutions for backward stochastic Volterra integral equations in Lp spaces, extending previous results to broader conditions and solution types.

## Contribution

It generalizes the solvability results of BSVIEs to Lp spaces for both M-solutions and adapted solutions, broadening the theoretical framework.

## Key findings

- Proves existence and uniqueness of M-solutions in Lp for 1<p<2.
- Establishes unique solvability of adapted solutions in Lp for p>1.
- Extends previous results to more general Lp spaces.

## Abstract

This paper is devoted to the unique solvability of backward stochastic Volterra integral equations (BSVIEs for short), in terms of both M-solution introduced in [15] and the adapted solutions in [6], [11]. We prove the existence and uniqueness of M-solutions of BSVIEs in Lp (1<p<2), which extends the results in [15]. The unique solvability of adapted solutions of BSVIEs in Lp (p>1) is also considered, which also generalize the results in [6] and [11].