Portfolio optimization based on bi-objective linear programming

In this study, we deal with a portfolio optimization problem including both risky and risk-free assets. We use the infinity norm criterion to measure portfolio risk and formulate the problem as a bi-objective linear optimization problem. Then, a single objective linear program is considered related to the bi-objective optimization problem. Using the well-known Karush-Kuhn-Tucker optimality conditions, we obtain analytic formula for an optimal solution. Moreover, we determine the whole efficient frontier by multi-criteria optimization techniques. Based on the theoretical results, two algorithms are proposed for finding the portfolio weights and the efficient frontier. Numerical examples are given for illustrating the new models and algorithms. Additionally, a simulation study has been conducted to assess the performance of the proposed method.