Portfolio Selection with Different Borrowing-Lending Rates: Utility Maximization Model based on Mean and VaR

This article investigates a portfolio selection problem with different borrowing–lending rates and with Value-at-Risk (VaR) as the measure of risk. The problem is formulated as a utility maximization model with a general utility function that is a function of only the mean and the VaR of portfolio return. Several properties of the efficient frontier of the mean-VaR model are first obtained and then used to give some existence conditions and characterizations of the optimal solution to the utility maximization model. Further, a solution method and a numerical algorithm for solving the optimal solution are proposed. Finally, a numerical example using the real data of Chinese stock market is given to show the validity and the practicability of these results.