Symmetry and order in the portfolio allocation problem
type: Item
instance of: scholarly article
title: Symmetry and order in the portfolio allocation problem
zbMATH Open document ID: 1013.91051
author: Harvey E. Lapan
author: David A. Hennessy
published in: Economic Theory
publication date: 2002-06-04T00:00:00Z
review text: In a single period model of a securities market with a finite number of assets, the classical portfolio allocation problem can be described as the problem of choosing the best portfolio for maximizing the expected utility of terminal wealth. If the asset returns are independently distributed and ordered (either in the likelihood ratio order or the reversed hazard order) then the optimum portfolio choices are also ordered for some classes of decision makers (for instance, those with non-decreasing and continuously differentiable utility functions). The present article extends these findings to the case of multivariate asset returns distributions that present certain kinds of symmetry structure. First they work with multivariate arrangement increasing density functions that allow strictly controlled asymmetries into the distribution of the rates of returns. Then, by considering permutation symmetric random returns, they place the asymmetry in the mappings of random draws on the rates of return that enter the terminal payoff in the utility function. Theses symmetries and asymmetries in the distribution structure are critical to understand optimum portfolio allocations even in the presence of a risk-free asset.
reviewed by: Miguel Ángel Mirás Calvo
Mathematics Subject Classification ID: 91B28
zbMATH DE Number: 1748973
zbMATH Keywords: portfolio allocation problem
zbMATH Keywords: multivariate distribution of asset returns
zbMATH Keywords: arrangement decreasing functions
zbMATH Keywords: permutation symmetric functions
zbMATH Keywords: ordinal structure of optimal portfolios
MaRDI profile type: Publication
full work available at URL: s001990100170
OpenAlex ID: W2159517887
DOI: 10.1007/S001990100170
description: scientific article; zbMATH DE number 1748973