A decomposition method for optimal portfolios with regime-switching and risk constraint

Jingzhen Liu; Ka Fai Cedric Yiu; Tak Kuen Siu

doi:10.3233/RDA-2012-0070

A decomposition method for optimal portfolios with regime-switching and risk constraint

Jingzhen Liu, Ka Fai Cedric Yiu, Tak Kuen Siu

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

We study an optimal investment problem for an investor who faces a dynamic risk constraint in a Markovian regime-switching environment. The goal of the investor is to maximize the expected utility of terminal wealth subject to the dynamic risk constraint specified by a proportional Value at Risk (VaR). By transforming the stochastic optimal control problem associated with the optimal investment problem into a deterministic control problem, we obtain a closed-form solution to the optimal investment problem for the case of a power utility. To evaluate the value function, we employ a numerical approximation method based on a piecewise constant approximation to the modulating Markov chain. A numerical example is given to illustrate the impact of the dynamic risk constraint on the optimal investment strategy.

Original language	English
Pages (from-to)	269-276
Number of pages	8
Journal	Risk and Decision Analysis
Volume	3
Issue number	4
DOIs	https://doi.org/10.3233/RDA-2012-0070
Publication status	Published - 17 Dec 2012

Keywords

dynamic risk constraint
martingale transform
Optimal portfolio selection
piecewise constant approximation
power utility
regime switching

ASJC Scopus subject areas

Economics and Econometrics
Finance
Statistics, Probability and Uncertainty
Statistics and Probability

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10.3233/RDA-2012-0070

Cite this

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abstract = "We study an optimal investment problem for an investor who faces a dynamic risk constraint in a Markovian regime-switching environment. The goal of the investor is to maximize the expected utility of terminal wealth subject to the dynamic risk constraint specified by a proportional Value at Risk (VaR). By transforming the stochastic optimal control problem associated with the optimal investment problem into a deterministic control problem, we obtain a closed-form solution to the optimal investment problem for the case of a power utility. To evaluate the value function, we employ a numerical approximation method based on a piecewise constant approximation to the modulating Markov chain. A numerical example is given to illustrate the impact of the dynamic risk constraint on the optimal investment strategy.",

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A decomposition method for optimal portfolios with regime-switching and risk constraint

Abstract

Keywords

ASJC Scopus subject areas

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