Portfolio optimization based on bi-objective linear programming

Abstract

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.