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

Riu Naito; Toshihiro Yamada

doi:10.1515/mcma-2019-2053

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

Riu Naito^*, Toshihiro Yamada

^*Corresponding author for this work

Department of Economics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	341-361
Number of pages	21
Journal	Monte Carlo Methods and Applications
Volume	25
Issue number	4
DOIs	https://doi.org/10.1515/mcma-2019-2053
State	Published - 2019/12/01

Keywords

Backward stochastic differential equation
Malliavin calculus
second-order discretization

ASJC Scopus subject areas

Statistics and Probability
Applied Mathematics

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10.1515/mcma-2019-2053

Cite this

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title = "A second-order discretization for forward-backward SDEs using local approximations with Malliavin calculus",

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.",

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author = "Riu Naito and Toshihiro Yamada",

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AU - Yamada, Toshihiro

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N2 - 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.

AB - 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.

KW - Backward stochastic differential equation

KW - Malliavin calculus

KW - second-order discretization

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

Abstract

Keywords

ASJC Scopus subject areas

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