A Numerical Scheme for BSVIEs

TL;DR

This paper develops a numerical Euler scheme for backward stochastic Volterra integral equations, approximating them via BSDEs and achieving a global 1/2 order convergence in L^2 norm.

Contribution

It introduces a novel numerical method combining approximation by BSDEs and Euler solutions, providing a convergence rate analysis for BSVIEs.

Findings

Achieves global 1/2 order convergence in L^2 norm.

Provides a practical numerical scheme for BSVIEs.

Demonstrates effectiveness through theoretical analysis.

Abstract

In this paper, we consider the Euler method for backward stochastic Volterra integral equations. First, we approximate the original equation by a family of backward stochastic equations (BSDEs, for short). Then we solve the BSDEs by the Euler method. Finally, by virtue of the numerical solutions to BSDEs, we get the numerical solution to original equation and obtain the global $1/2$ order convergence speed in $L^2$ norm.