Optimizing Measures of Risk: A Simplex-like Algorithm

Alejandro Balbás (), Raquel Balbás Universidad and Silvia Mayoral
Additional contact information
Alejandro Balbás: Universidad Carlos III
Raquel Balbás Universidad: Autónoma de Madrid

No 11/06, Faculty Working Papers from School of Economics and Business Administration, University of Navarra

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.

Keywords: Risk; Measure.; Deviation; Measure.; Portfolio; Selection.; Infinite-Dimensional; Linear; Programming.; Simpl (search for similar items in EconPapers)
JEL-codes: C02 G11 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2006-09-02
New Economics Papers: this item is included in nep-fin, nep-fmk, nep-rmg and nep-upt
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Forthcoming, European Journal of Operational Research

Downloads: (external link)
http://www.unav.edu/documents/10174/6546776/1158074034_wp1106.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:una:unccee:wp1106

Access Statistics for this paper

More papers in Faculty Working Papers from School of Economics and Business Administration, University of Navarra
Bibliographic data for series maintained by ().