An interactive compromise programming for portfolio investment problem

This paper addresses an approach for solving multicriteria portfolio investment problem. The original Markowitz mean-variance model is formulated as a problem of bi-objective optimization with linear and quadratic objective functions. In the current work, this model is extended by introducing a new objective, reflecting asset properties that are useful for the portfolio allocation process. A method based on parameterized achievement scalarizing function is applied to produce Pareto optimal portfolios. A mathematical programming formulation that allows for solving the problem with conventional optimization methods is presented. In addition, a method of reflecting the decision maker’s preferences by means of changing the weights in the achievement scalarizing functions is introduced. A decision making process is simulated for the three-objective portfolio optimization problem.