A stochastic maximum principle for a Markov regime-switching jump-diffusion model and its application to finance

Xin Zhang; Robert J. Elliott; Tak Kuen Siu

doi:10.1137/110839357

A stochastic maximum principle for a Markov regime-switching jump-diffusion model and its application to finance

Xin Zhang^*, Robert J. Elliott, Tak Kuen Siu

^*Corresponding author for this work

Department of Applied Finance

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

85 Citations (Scopus)

184 Downloads (Pure)

Abstract

This paper develops a sufficient stochastic maximum principle for a stochastic optimal control problem, where the state process is governed by a continuous-time Markov regime-switching jump-diffusion model. We also establish the relationship between the stochastic maximum principle and the dynamic programming principle in a Markovian case. Applications of the stochastic maximum principle to the mean-variance portfolio selection problem are discussed.

Original language	English
Pages (from-to)	964-990
Number of pages	27
Journal	SIAM Journal on Control and Optimization
Volume	50
Issue number	2
DOIs	https://doi.org/10.1137/110839357
Publication status	Published - 2012

Bibliographical note

Copyright SIAM Publications. Article archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further information see http://www.siam.org/.

Access to Document

10.1137/110839357

Publisher version (open access).pdfFinal published version, 367 KB

Cite this

@article{a9676655ea29495a98314dc10f70ced8,

title = "A stochastic maximum principle for a Markov regime-switching jump-diffusion model and its application to finance",

abstract = "This paper develops a sufficient stochastic maximum principle for a stochastic optimal control problem, where the state process is governed by a continuous-time Markov regime-switching jump-diffusion model. We also establish the relationship between the stochastic maximum principle and the dynamic programming principle in a Markovian case. Applications of the stochastic maximum principle to the mean-variance portfolio selection problem are discussed.",

author = "Xin Zhang and Elliott, {Robert J.} and Siu, {Tak Kuen}",

note = "Copyright SIAM Publications. Article archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further information see http://www.siam.org/.",

year = "2012",

doi = "10.1137/110839357",

language = "English",

volume = "50",

pages = "964--990",

journal = "SIAM Journal on Control and Optimization",

issn = "0363-0129",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}

TY - JOUR

T1 - A stochastic maximum principle for a Markov regime-switching jump-diffusion model and its application to finance

AU - Zhang, Xin

AU - Elliott, Robert J.

AU - Siu, Tak Kuen

N1 - Copyright SIAM Publications. Article archived for private and non-commercial use with the permission of the author and according to publisher conditions. For further information see http://www.siam.org/.

PY - 2012

Y1 - 2012

N2 - This paper develops a sufficient stochastic maximum principle for a stochastic optimal control problem, where the state process is governed by a continuous-time Markov regime-switching jump-diffusion model. We also establish the relationship between the stochastic maximum principle and the dynamic programming principle in a Markovian case. Applications of the stochastic maximum principle to the mean-variance portfolio selection problem are discussed.

AB - This paper develops a sufficient stochastic maximum principle for a stochastic optimal control problem, where the state process is governed by a continuous-time Markov regime-switching jump-diffusion model. We also establish the relationship between the stochastic maximum principle and the dynamic programming principle in a Markovian case. Applications of the stochastic maximum principle to the mean-variance portfolio selection problem are discussed.

UR - http://www.scopus.com/inward/record.url?scp=84861586721&partnerID=8YFLogxK

U2 - 10.1137/110839357

DO - 10.1137/110839357

M3 - Article

AN - SCOPUS:84861586721

SN - 0363-0129

VL - 50

SP - 964

EP - 990

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 2

ER -

A stochastic maximum principle for a Markov regime-switching jump-diffusion model and its application to finance

Abstract

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this