Backward stochastic Volterra integral equations with jumps in a general filtration

TL;DR

This paper extends the theory of backward stochastic Volterra integral equations with jumps to general filtrations, establishing existence, uniqueness, comparison results, and exploring solution regularity in the jump setting.

Contribution

It introduces new existence, uniqueness, and comparison results for these equations under general filtrations and analyzes solution regularity with Lp-data in the jump setting.

Findings

Extended existence and uniqueness results to general filtrations.

Established comparison theorems for backward stochastic Volterra equations.

Analyzed time regularity of solutions with Lp-data in the jump setting.

Abstract

In this paper, we study backward stochastic Volterra integral equations introduced in [26, 45] and extend the existence, uniqueness or comparison results for general filtration as in [31] (not only Brownian-Poisson setting). We also consider Lp-data and explore the time regularity of the solution in the It{\^o} setting, which is also new in this jump setting.