Optimizing Measures of Risk: A Simplex-like Algorithm

Balbás, Alejandro; Balbás, Raquel; Mayoral, Silvia

Publication:
Optimizing Measures of Risk: A Simplex-like Algorithm

dc.affiliation.dpto	UC3M. Departamento de Economía de la Empresa	es
dc.contributor.author	Balbás, Alejandro
dc.contributor.author	Balbás, Raquel
dc.contributor.author	Mayoral, Silvia
dc.contributor.other	Universidad de Navarra. Facultad de Ciencias Económicas y Empresariales
dc.date.accessioned	2010-01-20T09:30:16Z
dc.date.available	2010-01-20T09:30:16Z
dc.date.issued	2006-09
dc.description.abstract	The minimization of general risk or dispersion measures is becoming more and more important in Portfolio Choice Theory. There are two major reasons. Firstly, the lack of symmetry in the returns of many assets provokes that the classical optimization of the standard deviation may lead to dominated strategies, from the point of view of the second order stochastic dominance. Secondly, but not less important, many institutional investors must respect legal capital requirements, which may be more easily studied if one deals with a risk measure related to capital losses. This paper proposes a new method to simultaneously minimize several risk or dispersion measures. The representation theorems of risk measures are applied to transform the general risk minimization problem in a minimax problem, and later in a linear programming problem between infinite-dimensional Banach spaces. Then, new necessary and sufficient optimality conditions are stated and a simplex-like algorithm is developed. The algorithm solves the dual (and therefore the primal) problem and provides both optimal portfolios and their sensitivities. The approach is general enough and does not depend on any particular risk measure, but some of the most important cases are specially analyzed.
dc.format.mimetype	application/pdf
dc.identifier.uri	https://hdl.handle.net/10016/6534
dc.language.iso	eng
dc.relation.ispartofseries	11/06
dc.rights	Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.accessRights	open access
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.eciencia	Empresa
dc.subject.other	Risk Measure
dc.subject.other	Deviation Measure
dc.subject.other	Portfolio Selection
dc.subject.other	Infinite- Dimensional Linear Programming
dc.subject.other	Simplex-Like Method
dc.title	Optimizing Measures of Risk: A Simplex-like Algorithm
dc.type	working paper	*
dspace.entity.type	Publication