Model and upper-lower bound estimation scheme for portfolio optimisation considering uncertain investment time horizon

In this paper, we study the portfolio selection problem considering the uncertain investment time horizon. We employ the Period Value at Risk (PVaR) to characterise the risk in the special cases and establish a fundamental mixed integer linear programming (MILP) model to obtain the optimal portfolio solutions. Identifying that the symmetric property of PVaR can significantly reduce the computation burden of the CPLEX solver, an enhanced MILP model is proposed. To verify the quality of obtained solutions, we also develop fast lower and upper bound estimation schemes respectively. Using the real-world data sets from NYSE and NASDAQ stock markets, numerical results are provided to show the efficiency of the enhanced model.