Optimal portfolios with maximum Value-at-Risk constraint under a hidden Markovian regime-switching model

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.