This paper deals with the mathematics of the Markowitz theory of portfolio management. Let E and V be two homogeneous functions defined on ℝⁿ, the first linear, the other positive definite quadratic. Furthermore let Δ be a simplex contained in ℝⁿ (the set of admissible portfolios), for example Δ : x₁+ ... + xₙ = 1, . Our goal is to investigate the properties of the restricted mappings (V,E):Δ → ℝ² (the so called Markowitz mappings) and to classify them. We introduce the notion of a generic model (Δ,E,V) and investigate the equivalence of such models defined by continuous deformation.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am30-2-6,
author = {Piotr Jaworski},
title = {A geometric point of view on mean-variance models},
journal = {Applicationes Mathematicae},
volume = {30},
year = {2003},
pages = {217-241},
zbl = {1068.91032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-2-6}
}
Piotr Jaworski. A geometric point of view on mean-variance models. Applicationes Mathematicae, Tome 30 (2003) pp. 217-241. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-2-6/