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

93 Citations (Scopus)

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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/.

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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.

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

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