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.
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Bibliographic InfoArticle provided by Elsevier in its journal European Journal of Operational Research.
Volume (Year): 192 (2009)
Issue (Month): 2 (January)
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Web page: http://www.elsevier.com/locate/eor
Risk measure Deviation measure Portfolio selection Infinite-dimensional linear programming Simplex-like method;
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- Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Risk Measures," Risk and Insurance 0407002, EconWPA.
- 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.
- Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
- 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.
- 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.
- 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.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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