Optimal portfolios with regime-switching and Value-at-Risk constraint

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)


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
Issue number6
Publication statusPublished - Jun 2010


Dive into the research topics of 'Optimal portfolios with regime-switching and Value-at-Risk constraint'. Together they form a unique fingerprint.

Cite this