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: email@example.com
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
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