A geometric point of view on mean-variance models

Volume 30 / 2003

Piotr Jaworski Applicationes Mathematicae 30 (2003), 217-241 MSC: Primary 91B28; Secondary 58K30, 14P99, 90C20. DOI: 10.4064/am30-2-6


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.


  • Piotr JaworskiInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

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