Solvability of general backward stochastic Volterra integral equation with non-Lipschitz coefficients

TL;DR

This paper establishes the existence and uniqueness of solutions for general backward stochastic Volterra integral equations with non-Lipschitz coefficients, extending previous results and using more concise methods.

Contribution

It provides new existence and uniqueness results for BSVIEs with non-Lipschitz conditions, broadening the scope of solvability theory.

Findings

Unique solvability of M-solutions under non-Lipschitz conditions

Unique solutions for adapted solutions with more general stochastic conditions

Extension of previous solvability results to broader classes of BSVIEs

Abstract

In this paper we study the unique solvability of backward stochastic Volterra integral equations (BSVIEs in short), in terms of both the M-solutions introduced in [17] and the adapted solutions in [6], [12] or [14]. A general existence and uniqueness of M-solutions is proved under non-Lipschitz conditions by virtue of a briefer argument than the one in [17], which also extends the results in [17]. For the adapted solutions, the unique solvability of BSVIEs, under more general stochastic non-Lipschitz conditions, is obtained which generalizes the results in [6], [12] and [14].