Distortion Risk Measures in Portfolio Optimization
Distortion risk measures are perspective risk measures because they allow an asset manager to reflect a client’s attitude toward risk by choosing the appropriate distortion function. In this paper, the idea of asymmetry was applied to the standard construction of distortion risk measures. The new asymmetric distortion risk measures are derived based on the quadratic distortion function with different risk-averse parameters.
KeywordsRisk Measure Portfolio Optimization Stochastic Dominance Distortion Function Coherent Risk Measure
Unable to display preview. Download preview PDF.
- Adam A., Houkari M. and Laurent J., 2007, Spectral Risk Measures and Portfolio Selection, http://hal.archives-ouvertes.fr/docs/00/16/56/41/PDF/Adam-Houkari-Laurent-ISFA-WP2037.pdf .
- Albrecht P., 2004, Risk measures, in Encyclopedia of Actuarial Science, Wiley, New York.Google Scholar
- Balbas A., Garrido J. and Mayoral S., 2007, Properties of Distortion Risk Measures, available at http://www.gloriamundi.org/picsresources/bgm_pdr.pdf .
- Balzer L., 2001, Investment risk: a unified approach to upside and downside returns, in Managing DownsideRisk in Financial Markets: Theory, Practice and Implementation, eds. Sortino F. and Satchell S., 103–105. Oxford: Butterworth-Heinemann.Google Scholar
- Bellini F. and Caperdoni C., 2006, Coherent distortion risk measures and higher order stochastic dominances, preprint, January 2006, available at http://www.gloriamundi.org .
- Chekhlov A., Uryasev S. and Zabarankin M., 2003, Portfolio optimization with Drawdown constraints, Implemented in Portfolio Safeguard by AORDA.com, Theory Probability Application 44(1).Google Scholar
- Denneberg D., 1990, Distorted probabilities and insurance premiums, Methods of Operations Research 63, 3–5.Google Scholar
- Denneberg D., 1994, Non-Additive Measures and Integrals. Dordrecht: Kluwer.Google Scholar
- Dhaene J., Goovaerts M. and Kaas R., 2003, Economic capital allocation derived from risk measures, North American Actuarial Journal 7(2), 44–59.Google Scholar
- Ebert U., 2005, Measures of downside risk, Economics Bulletin, Economics Bulletin 4(16), 1–9.Google Scholar
- Embrechts P., McNeal A. and Straumann D., 2002, Correlation and dependence in risk management: properties and pitfalls, in Risk Management: Value at Risk and Beyond, ed. Dempste M.A.H., 176–223. Cambridge: Cambridge University Press.Google Scholar
- Fabozzi F. and Tunaru R., 2008, Pricing Models for Real Estate Derivatives, Yale Working paper.Google Scholar
- Föllmer H. and Schied, A., 2002b, Robust preferences and convex measures of risk, in Advances in Finance and Stochastics, eds. Sandmann K. and Schonbucher P. J., 39–56. New York: Springer.Google Scholar
- Frittelli M. and Rosazza Gianin E., 2005, Law invariant convex risk measures, Advances in Finance and Stochastics 7, 33–46.Google Scholar
- Gaivoronski A. and Pflug G., 2005, Value at Risk in Portfolio Optimization: Properties and Computational Approach, Journal of Risk, 7, 1–31.Google Scholar
- Giacometti R. and Ortobelli S., 2004, Risk measures for asset allocation models, in Risk Measures for the 21st Century, ed. Szegö G., 69–87. Chichester: Wiley.Google Scholar
- Goovaerts M., De Vijlder F. and Haezendonck J., 1984, Insurance Premiums. Amsterdam: North-Holland.Google Scholar
- Gourieroux C. and Liu W., 2006, Efficient portfolio analysis using distortion risk measures, Les Cahiers du CREF 06–35.Google Scholar
- Hadar J. and Russell W., 1969, Rules for ordering uncertain prospects, American Economic Review 59, 25–34.Google Scholar
- Hardy M. and Wirch J., 2003, Ordering of risk measures for capital adequacy, in Proceedings of the AFIR Colloquim, Tromsoe.Google Scholar
- Heyde C., Kou S. and Peng X., 2006, What Is a Good Risk Measure: Bridging the Gaps Between Data, Coherent Risk Measure, and Insurance Risk Measure, Columbia University.Google Scholar
- Hürlimann W., 2004, Distortion risk measures and economic capital, North American Actuarial Journal 8(1), 86–95.Google Scholar
- Kaas R., Van Heerwaarden A. and Goovaerts M., 1994, Ordering of actuarial risks, CAIRE Educations Series, Brussels.Google Scholar
- Kaas R., Goovaerts M., Dhaene J. and Denuit M., 2001, Modern actuarial risk theory. Dordrecht: Kluwer.Google Scholar
- Kusuoka E., 2001, Law invariant risk measures have the Fatou property, preprint, Universite Paris Dauphine.Google Scholar
- Ortobelli S., Rachev S., Shalit H. and Fabozzi F., 2008, Risk Probability Functionals and Probability Metrics in Portfolio Theory, Probability and Mathematical Statistics, 28, 203–234.Google Scholar
- Rachev R., Ortobelli S., Stoyanov S., Fabozzi F. and Biglova A., 2008, Desirable properties of an ideal risk measure in portfolio theory, International Journal of Theoretical and Applied Finance. Google Scholar
- Rockafellar R., Uryasev S. and Zabarankin M., 2002, Deviation measures in generalized linear regression, Risk Management and Financial Lab.Google Scholar
- Rockafellar R., Uryasev S. and Zabarankin M., 2003, Deviation measures in risk analysis and optimization, Risk Management and Financial Engineering Lab.Google Scholar
- Rothschild M. and Stiglitz J., 1970, Increasing risk. I.a. definition, Journal of Economic Theory 2, 225–243.Google Scholar
- Szegö G., 2004, On the (non)acceptance of innovations, in Risk Measures for the 21st Century, ed., Szegö G., 1–10. Chichester: Wiley.Google Scholar
- Tsanakas A. and Desli E., 2003, Risk measures and theories of choice, British Actuarial Journal 9, 959–981.Google Scholar
- Wang S., 2002, A risk measure that goes beyond coherence, 12th AFIR International Colloquium, Mexico.Google Scholar
- Wang S., 2004, Cat bond pricing using probability transforms, Geneva Papers, Special issue on Insurance and the State of the Art in Cat Bond Pricing 278, 19–29.Google Scholar
- Zhang Y. and Rachev S., 2006, Risk Attribution and Portfolio Performance Measurement: An Overview, Journal of Applied Functional Analysis, 4, 373–402.Google Scholar