A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus

Author:

Naito Riu,Yamada Toshihiro

Abstract

Abstract The paper proposes a new second-order discretization method for forward-backward stochastic differential equations. The method is given by an algorithm with polynomials of Brownian motions where the local approximations using Malliavin calculus play a role. For the implementation, we introduce a new least squares Monte Carlo method for the scheme. A numerical example is illustrated to check the effectiveness.

Funder

Japan Society for the Promotion of Science

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Statistics and Probability

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Deep Learning-Based Expansion Around Elliptic Diffusions;2023 IEEE Asia-Pacific Conference on Computer Science and Data Engineering (CSDE);2023-12-04

2. Numerical methods for backward stochastic differential equations: A survey;Probability Surveys;2023-01-01

3. A deep learning-based high-order operator splitting method for high-dimensional nonlinear parabolic PDEs via Malliavin calculus: application to CVA computation;2022 IEEE Symposium on Computational Intelligence for Financial Engineering and Economics (CIFEr);2022-05

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