Approximations for adapted M-solutions of type-II backward stochastic Volterra integral equations

¹ Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama-cho, Toyonaka, Osaka 560-8531, Japan
² Research Institute for Interdisciplinary Science, Department of Mathematics, Okayama University, 3-1-1 Tsushima-naka, Kita-ku Okayama 700-8530, Japan

^* Corresponding author: hmgch2950@gmail.com

Received: 8 July 2021
Accepted: 11 November 2022

Abstract

In this paper, we study a class of Type-II backward stochastic Volterra integral equations (BSVIEs). For the adapted M-solutions, we obtain two approximation results, namely, a BSDE approximation and a numerical approximation. The BSDE approximation means that the solution of a finite system of backward stochastic differential equations (BSDEs) converges to the adapted M-solution of the original equation. As a consequence of the BSDE approximation, we obtain an estimate for the L²-time regularity of the adapted M-solutions of Type-II BSVIEs. For the numerical approximation, we provide a backward Euler-Maruyama scheme, and show that the scheme converges in the strong L²-sense with the convergence speed of order 1/2. These results hold true without any differentiability conditions for the coefficients.