Generalization by Optimization in Menger Probabilistic Normed Spaces with Application on Portfolio in Insurance

Abstract

The purpose of this paper is to show that the category of normed spaces can be embedded in the category of Menger probabilistic normed spaces, and that C( Ω ) is probabilistic normable, whereas it is not normable in the classical case, when Ω is an open subset of Rn. So, the spectrum of the category of Menger probabilistic normed spaces is broader than the category of classical normed spaces. Therefore, it can be a meaningful replacement in some model of security markets. As our model is suitably generalized, that fact can help us to adapt and improve within natural problems of finance, especially, in portfolio optimization of insurance.