Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm
AbstractThe minimization of general risk functions is becoming more and more important in portfolio choice theory and optimal hedging. There are two major reasons. Firstly, heavy tails and 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 general risk or dispersion measures. The representation theorems of risk functions 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 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. A final real data numerical example illustrates the practical performance of the proposed methodology.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 192 (2009)
Issue (Month): 2 (January)
Contact details of provider:
Web page: http://www.elsevier.com/locate/eor
Risk measure Deviation measure Portfolio selection Infinite-dimensional linear programming Simplex-like method;
Other versions of this item:
- Balbás, Alejandro & Balbás, Raquel & Mayoral, Silvia, 2009. "Portfolio choice and optimal hedging with general risk functions: a simplex-like algorithm," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/13054, Universidad Carlos III de Madrid.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Balbas, Alejandro & Heras, Antonio, 1993. "Duality theory for infinite-dimensional multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 68(3), pages 379-388, August.
- Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
- Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Risk Measures," Risk and Insurance 0407002, EconWPA.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- W. Ogryczak & A. Ruszczynski, 1997.
"From Stochastic Dominance to Mean-Risk Models: Semideviations as Risk Measures,"
ir97027, International Institute for Applied Systems Analysis.
- Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
- Barber, Joel R. & Copper, Mark L., 1998. "A minimax risk strategy for portfolio immunization," Insurance: Mathematics and Economics, Elsevier, vol. 23(2), pages 173-177, November.
- Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
- Alexander, S. & Coleman, T.F. & Li, Y., 2006. "Minimizing CVaR and VaR for a portfolio of derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 583-605, February.
- Benati, Stefano, 2003. "The optimal portfolio problem with coherent risk measure constraints," European Journal of Operational Research, Elsevier, vol. 150(3), pages 572-584, November.
- Alejandro BalbÃ¡s & Raquel BalbÃ¡s, 2009. "Compatibility between pricing rules and risk measures: The CCVaR," Business Economics Working Papers wb090201, Universidad Carlos III, Departamento de Economía de la Empresa.
- Assa, Hirbod & Balbás, Alejandro, 2011. "Good Deals and compatible modification of risk and pricing rule: a regulatory treatment," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/12967, Universidad Carlos III de Madrid.
- Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2010. "Minimizing measures of risk by saddle point conditions," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/12974, Universidad Carlos III de Madrid.
- Balbás, Alejandro & Balbás, Raquel & Garrido, José, 2010. "Extending pricing rules with general risk functions," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/12956, Universidad Carlos III de Madrid.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.