Geodesic
On a generalization of Markowitz preference relation
Serdica Mathematical Journal, Tome 43 (2017) no. 3-4, pp. 211-220.

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Given two families u = (up)p∈I and v = (vq)q∈J of real continuous functions on a topological space X, we define a preorder R = R(u, v) on X by the condition that any member of u is an R-increasing and any member of v is an R-decreasing function. It turns out that if the topological space X is quasi-compact and sequentially compact, then any element x ∈ X is R-dominated by an R-maximal element m ∈ X: xRm. In particular, since the (n − 1)-dimensional simplex is a compact subset of R^n , then considering its members as portfolios consisting of n financial assets, we obtain the classical 1952 result of Harry Markowitz that any portfolio is dominated by an efficient portfolio. Moreover, several other examples of possible application of this general setup are presented.
Keywords: mean-variance theory, efficient financial portfolio, Markowitz preference relation, topological space, 06A99, 54A20, 91G10 
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Iliev, Valentin Vankov. On a generalization of Markowitz preference relation. Serdica Mathematical Journal, Tome 43 (2017) no. 3-4, pp. 211-220. http://geodesic.mathdoc.fr/item/SMJ2_2017_43_3-4_a0/