## 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.

Original language | English |
---|---|

Pages (from-to) | 19-79 |

Number of pages | 61 |

Journal | ESAIM - Probability and Statistics |

Volume | 27 |

DOIs | |

Publication status | Published - 2023 |

## Keywords

- Adapted M-solutions
- Backward stochastic Volterra integral equations
- BSDE approximations
- Euler-Maruyama scheme
- L2-time regularity

## ASJC Scopus subject areas

- Statistics and Probability