A parametric convex programming approach applied to portfolio pelection problems with fuzzy costs

In this work we consider the portfolio selection problems with uncertainties as a kind of multiple objective problem with fuzzy costs in the objective functions. The portfolio selection problems can be classified as convex programming problems. Although convex programming problems are a special class of nonlinear programming, they can also be defined as a general linear programming problem. These problems are of utmost importance in a variety of relevant practical fields. In addition, since ambiguity and vagueness are natural and ever-present in real-life situations requiring solutions, it makes perfect sense to attempt to address them using fuzzy convex programming technique. This work presents a novel fuzzy set based method that solves a class of convex programming problems with vagueness costs in the objective functions. This method transforms a fuzzy convex multi-objective programming problem into a parametric convex multi-objective programming one. When obtain the efficient solutions of the transformed problem, they satisfy an aspiration level defined by a decision maker. This proposed method is applied in two portfolio selection numerical examples by using Latibex data of some Brazilian securities.