Positivity-preserving numerical schemes for stochastic differential equations

Keisuke Abiko; Tetsuya Ishiwata

doi:10.1007/s13160-022-00554-7

Positivity-preserving numerical schemes for stochastic differential equations

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

Abstract

The solutions of stochastic differential equations arising in biology, finance and so on often have positivity. However, numerical solutions by the standard schemes often fail to satisfy this property. In this paper, we propose positivity-preserving numerical schemes for stochastic differential equations by virtue of Itô’s formula. We also show the convergence result of the proposed scheme and demonstrate their effectiveness by numerical examples.

Original language	English
Pages (from-to)	1095-1108
Number of pages	14
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	39
Issue number	3
DOIs	https://doi.org/10.1007/s13160-022-00554-7
Publication status	Published - 2022 Dec

Keywords

34F05
60H10
65C30
Numerical scheme
Positivity-preserving scheme
Stochastic differential equation

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

Access to Document

10.1007/s13160-022-00554-7

Cite this

@article{b0da3a29985e48f085d5cb7f069189b3,

title = "Positivity-preserving numerical schemes for stochastic differential equations",

abstract = "The solutions of stochastic differential equations arising in biology, finance and so on often have positivity. However, numerical solutions by the standard schemes often fail to satisfy this property. In this paper, we propose positivity-preserving numerical schemes for stochastic differential equations by virtue of It{\^o}{\textquoteright}s formula. We also show the convergence result of the proposed scheme and demonstrate their effectiveness by numerical examples.",

keywords = "34F05, 60H10, 65C30, Numerical scheme, Positivity-preserving scheme, Stochastic differential equation",

author = "Keisuke Abiko and Tetsuya Ishiwata",

note = "Funding Information: This work was supported by KAKENHI No. 19H05599. Publisher Copyright: {\textcopyright} 2022, The JJIAM Publishing Committee and Springer Japan KK, part of Springer Nature.",

year = "2022",

month = dec,

doi = "10.1007/s13160-022-00554-7",

language = "English",

volume = "39",

pages = "1095--1108",

journal = "Japan Journal of Industrial and Applied Mathematics",

issn = "0916-7005",

publisher = "Springer Japan",

number = "3",

}

TY - JOUR

T1 - Positivity-preserving numerical schemes for stochastic differential equations

AU - Abiko, Keisuke

AU - Ishiwata, Tetsuya

PY - 2022/12

Y1 - 2022/12

N2 - The solutions of stochastic differential equations arising in biology, finance and so on often have positivity. However, numerical solutions by the standard schemes often fail to satisfy this property. In this paper, we propose positivity-preserving numerical schemes for stochastic differential equations by virtue of Itô’s formula. We also show the convergence result of the proposed scheme and demonstrate their effectiveness by numerical examples.

AB - The solutions of stochastic differential equations arising in biology, finance and so on often have positivity. However, numerical solutions by the standard schemes often fail to satisfy this property. In this paper, we propose positivity-preserving numerical schemes for stochastic differential equations by virtue of Itô’s formula. We also show the convergence result of the proposed scheme and demonstrate their effectiveness by numerical examples.

KW - 34F05

KW - 60H10

KW - 65C30

KW - Numerical scheme

KW - Positivity-preserving scheme

KW - Stochastic differential equation

UR - http://www.scopus.com/inward/record.url?scp=85141999230&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85141999230&partnerID=8YFLogxK

U2 - 10.1007/s13160-022-00554-7

DO - 10.1007/s13160-022-00554-7

M3 - Article

AN - SCOPUS:85141999230

VL - 39

SP - 1095

EP - 1108

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 3

ER -

Positivity-preserving numerical schemes for stochastic differential equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this