A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus-Reference-Cited by-同舟云学术

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

Published:2019-12-01 Issue:4 Volume:25 Page:341-361
ISSN:0929-9629
Container-title:Monte Carlo Methods and Applications
language:
Short-container-title:

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

Link

https://www.degruyter.com/document/doi/10.1515/mcma-2019-2053/pdf

Reference34 articles.

1. Second order discretization of backward SDEs and simulation with the cubature method;Ann. Appl. Probab.,2014

2. Second order discretization of backward SDEs and simulation with the cubature method;Ann. Appl. Probab.,2014

3. A third-order weak approximation of multidimensional Itô stochastic differential equations;Monte Carlo Methods Appl.,2019

4. Error expansion for the discretization of backward stochastic differential equations;Stochastic Process. Appl.,2007

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