Optimal portfolios with regime switching and value-at-risk constraint

Ka Fai Cedric Yiu, Jingzhen Liu, Tak Kuen Siu, Wai Ki Ching

Research output: Journal article publicationJournal articleAcademic researchpeer-review

42 Citations (Scopus)

Abstract

We consider the optimal portfolio selection problem subject to a maximum value-at-Risk (MVaR) constraint when the price dynamics of the risky asset are governed by a Markov-modulated geometric Brownian motion (GBM). Here, the market parameters including the market interest rate of a bank account, the appreciation rate and the volatility of the risky asset switch over time according to a continuous-time Markov chain, whose states are interpreted as the states of an economy. The MVaR is defined as the maximum value of the VaRs of the portfolio in a short time duration over different states of the chain. We formulate the problem as a constrained utility maximization problem over a finite time horizon. By utilizing the dynamic programming principle, we shall first derive a regime-switching Hamilton-Jacobi-Bellman (HJB) equation and then a system of coupled HJB equations. We shall employ an efficient numerical method to solve the system of coupled HJB equations for the optimal constrained portfolio. We shall provide numerical results for the sensitivity analysis of the optimal portfolio, the optimal consumption and the VaR level with respect to model parameters. These results are also used to investigating the effect of the switching regimes.
Original languageEnglish
Pages (from-to)979-989
Number of pages11
JournalAutomatica
Volume46
Issue number6
DOIs
Publication statusPublished - 1 Jun 2010

Keywords

  • Dynamic programming
  • Maximum value-at-risk constraints
  • Optimal portfolio selection
  • Regime-switching
  • Regime-switching HJB equations
  • Utility maximization

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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