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

被引：2

作者：

Hamaguchi, Yushi ^{[1
]}

Taguchi, Dai ^{[2
]}

机构：

[1] Osaka Univ, Grad Sch Engn Sci, Toyonaka, 1-3, Machikaneyama Cho, Osaka 5608531, Japan

[2] Okayama Univ, Res Inst Interdisciplinary Sci, Dept Math, 3-1-1 Tsushima Naka,Kita ku, Okayama 7008530, Japan

来源：

ESAIM-PROBABILITY AND STATISTICS | 2023年 / 27卷

关键词：

Backward stochastic Volterra integral equations; adapted M-solutions; BSDE approximations; Euler-Maruyama scheme; L-2-time regularity; L-P SOLUTIONS; DIFFERENTIAL-EQUATIONS; CONVERGENCE; DISCRETIZATION; ALGORITHM; SCHEME; JUMPS;

D O I：

10.1051/ps/2022017

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 L-2-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 L-2-sense with the convergence speed of order 1/2. These results hold true without any differentiability conditions for the coefficients.

引用

页码：19 / 79

页数：61

共 47 条

[1] Dynamic risk measure for BSVIE with jumps and semimartingale issues [J].