  In the portfolio multiobjective optimization framework, we propose to compare
and choose, among all feasible asset portfolios of a given market, the one that
maximizes the product of the distances between its values of risk and gain and
those of a suitable reference point (e.g., the so-called nadir). We show that
this approach has distinctive and remarkable features. While being not
influenced by how the objectives are scaled, it provides one with an efficient
(Pareto) portfolio that "dominates the most" with respect to the reference
point. Furthermore, although our no-preference strategy generally requires the
solution of a nonconvex (constrained) single-objective problem, we show how the
resulting (global) optimal portfolio can be easily and efficiently computed. We
also perform numerical tests based on some publicly available benchmark data
sets often used in the literature, highlighting the nice properties of our
approach.
