On the wavelet-based SWIFT method for backward stochastic differential equations

Ki Wai Chau; Cornelis W. Oosterlee

doi:10.1093/imanum/drx022

On the wavelet-based SWIFT method for backward stochastic differential equations

Ki Wai Chau^*, Cornelis W. Oosterlee

^*Corresponding author for this work

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

Abstract

We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate the problem of errors near the computation boundaries by means of an antireflective boundary technique, giving an improved approximation.We test our algorithm with different numerical experiments.

Original language	English
Pages (from-to)	1051-1083
Number of pages	33
Journal	IMA Journal of Numerical Analysis
Volume	38
Issue number	2
DOIs	https://doi.org/10.1093/imanum/drx022
Publication status	Published - 18 Apr 2018
Externally published	Yes

Bibliographical note

Funding Information:
EU Framework Programme for Research and Innovation Horizon 2020 (H2020-MSCA-ITN-2014, Project 643045, ‘EID WAKEUPCALL’).

Publisher Copyright:
© The authors 2017.

Funding

EU Framework Programme for Research and Innovation Horizon 2020 (H2020-MSCA-ITN-2014, Project 643045, ‘EID WAKEUPCALL’).

Keywords

antireflective boundary
backward stochastic differential equations
Fourier transform
Shannon wavelets

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10.1093/imanum/drx022

Cite this

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title = "On the wavelet-based SWIFT method for backward stochastic differential equations",

abstract = "We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate the problem of errors near the computation boundaries by means of an antireflective boundary technique, giving an improved approximation.We test our algorithm with different numerical experiments.",

keywords = "antireflective boundary, backward stochastic differential equations, Fourier transform, Shannon wavelets",

author = "Chau, {Ki Wai} and Oosterlee, {Cornelis W.}",

note = "Funding Information: EU Framework Programme for Research and Innovation Horizon 2020 (H2020-MSCA-ITN-2014, Project 643045, {\textquoteleft}EID WAKEUPCALL{\textquoteright}). Publisher Copyright: {\textcopyright} The authors 2017.",

year = "2018",

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doi = "10.1093/imanum/drx022",

language = "English",

volume = "38",

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AU - Chau, Ki Wai

AU - Oosterlee, Cornelis W.

N1 - Funding Information: EU Framework Programme for Research and Innovation Horizon 2020 (H2020-MSCA-ITN-2014, Project 643045, ‘EID WAKEUPCALL’). Publisher Copyright: © The authors 2017.

PY - 2018/4/18

Y1 - 2018/4/18

N2 - We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate the problem of errors near the computation boundaries by means of an antireflective boundary technique, giving an improved approximation.We test our algorithm with different numerical experiments.

AB - We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate the problem of errors near the computation boundaries by means of an antireflective boundary technique, giving an improved approximation.We test our algorithm with different numerical experiments.

KW - antireflective boundary

KW - backward stochastic differential equations

KW - Fourier transform

KW - Shannon wavelets

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JF - IMA Journal of Numerical Analysis

IS - 2

ER -

On the wavelet-based SWIFT method for backward stochastic differential equations

Abstract

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Keywords

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