Indeterminacy in portfolio selection

This paper develops the indeterminacy in “portfolio selection” putting together a modification of a device of measure theory used in our previous papers [Atti del XXI Convegno Annuale AMASES, 1997, pp. 635-647; Soft Computing in Financial Engineering, 1999, pp. 425-432] and Shannon's entropy of information. We obtain an expectation, variance and indeterminacy (E-V-I) functional which is a generalization of the expectation quadratic utility. If I=0 our model is more coherent with the expectation-variance (E-V) model than the classical model and if I≠0 our model yields a warning about the risk from indeterminacy that expectation quadratic utility model does not. A numerical method and its statistical application with Italian data illustrates the results.