## Abstract

This paper studies an optimal portfolio selection problem in the presence of the Maximum Value-at-Risk (MVaR) constraint in a hidden Markovian regime-switching environment. The price dynamics of n risky assets are governed by a hidden Markovian regime-switching model with a hidden Markov chain whose states represent the states of an economy. We formulate the problem as a constrained utility maximization problem over a finite time horizon and then reduce it to solving a Hamilton–Jacobi–Bellman (HJB) equation using the separation principle. The MVaR constraint for n risky assets plus one riskless asset is derived and the method of Lagrange multiplier is used to deal with the constraint. A numerical algorithm is then adopted to solve the HJB equation. Numerical results are provided to demonstrate the implementation of the algorithm.

Original language | English |
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Pages (from-to) | 194-205 |

Number of pages | 12 |

Journal | Automatica |

Volume | 74 |

DOIs | |

Publication status | Published - Dec 2016 |

## Keywords

- Hamilton-Jacobi-Bellman (HJB) equation
- Hidden Markov model (HMM)
- multiple risky assets
- Maximum Value-at-Risk (MVaR) constraint
- optimal portfolio