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Abstract

This paper deals with the mathematics of the Markowitz theory of portfolio management. Let $E$ and $V$ be two homogeneous functions defined on ${\Bbb R}^n$, the first linear, the other positive definite quadratic. Furthermore let ${\mit\Delta}$ be a simplex contained in ${\Bbb R}^n$ (the set of admissible portfolios), for example ${\mit\Delta} : x_1+ \dots + x_n =1$, $x_i \geq 0$. Our goal is to investigate the properties of the restricted mappings $(V,E):{\mit\Delta} \rightarrow {\Bbb R}^2$ (the so called Markowitz mappings) and to classify them. We introduce the notion of a generic model $({\mit\Delta}, E, V)$ and investigate the equivalence of such models defined by continuous deformation.