Volume 27, 2023
|Page(s)||19 - 79|
|Published online||06 January 2023|
Approximations for adapted M-solutions of type-II backward stochastic Volterra integral equations
Graduate School of Engineering Science, Osaka University,
2 Research Institute for Interdisciplinary Science, Department of Mathematics, Okayama University, 3-1-1 Tsushima-naka, Kita-ku Okayama 700-8530, Japan
* Corresponding author: firstname.lastname@example.org
Accepted: 11 November 2022
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.
Mathematics Subject Classification: 60H20 / 65C30 / 60H07
Key words: Backward stochastic Volterra integral equations / adapted M-solutions / BSDE approximations / Euler-Maruyama scheme / L2-time regularity
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.