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.

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].