A geometric point of view on mean-variance models

Piotr Jaworski¹

¹ Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland

Applicationes Mathematicae, Tome 30 (2003) no. 2, pp. 217-241.

Résumé

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.

Détail

DOI : 10.4064/am30-2-6

Keywords: paper deals mathematics markowitz theory portfolio management homogeneous functions defined bbb first linear other positive definite quadratic furthermore mit delta simplex contained bbb set admissible portfolios example mit delta dots geq investigate properties restricted mappings mit delta rightarrow bbb called markowitz mappings classify introduce notion generic model mit delta investigate equivalence models defined continuous deformation