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

Yushi Hamaguchi, Dai Taguchi

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)19-79
Number of pages61
JournalESAIM - Probability and Statistics
Publication statusPublished - 2023


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

ASJC Scopus subject areas

  • Statistics and Probability


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