Financial decisions based on zero-sum games : new conceptual and mathematical outcomes

All the n possible returns on a financial asset are the components of an element of a linear space over R. This paper shows how to transfer all these n possible returns on a one-dimensional straight line. In this research work, two or more than two financial assets are studied. More than two financial assets are always studied in pairs, so they are treated inside the budget set of a given decision-maker. Two univariate financial assets give rise to a bivariate financial asset characterized by a bivariate (two-dimensional) distribution of probability. This research work shows how constrained choices being made by a given decision-maker under conditions of uncertainty and riskiness maximize his utility of an ordinal nature. For this reason, prevision bundles are dealt with. Furthermore, every choice identifies a zero-sum game. Since a specific kind of choice associated with two or more than two objects is investigated, new conceptual and mathematical outcomes related to financial decisions are shown.