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 publicationJournal articleAcademic researchpeer-review


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 languageEnglish
Pages (from-to)269-276
Number of pages8
JournalRisk and Decision Analysis
Issue number4
Publication statusPublished - 17 Dec 2012


  • 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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