A formulation of portfolio selection problem with multiple criteria

Portfolio-type problems arise in many decision-making situations. In this paper, we consider these problems in the context of multiple criteria model that takes into account two types of criteria, which are used in decision maker's preferences: criteria of the first type are used to characterize both the entire portfolio and its individual elements, whereas criteria of the second type are solely used to evaluate the portfolio as a whole but not its elements. When formulating our multiple criteria model, we assume that criteria of the first type are quantitative and that they represent a higher priority for the decision maker compared to criteria of the second type. While we acknowledge the existence of other approaches, in this paper we focus on those portfolio selection problems that match the above structure of the criteria set. After formulating the portfolio selection problem, we offer a two-phase portfolio selection procedure that allows to choose an optimal portfolio by operating in two separate criteria spaces.