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DISTORTION RISK MEASURES, AMBIGUITY AVERSION AND OPTIMAL EFFORT

Published online by Cambridge University Press:  04 February 2014

Christian Y. Robert  and
Pierre-E. Therond
Christian Y. Robert*
Affiliation:
Institut de Science Financière et d'Assurances, Université de Lyon, Université Lyon 1, 50 Avenue Tony Garnier, F-69007 Lyon, France
Pierre-E. Therond
Affiliation:
Institut de Science Financière et d'Assurances, Université de Lyon, Université Lyon 1, 50 Avenue Tony Garnier, F-69007 Lyon, France, Galea & Associés – 91 rue de Rennes – F-75006Paris E-mail: pierre@therond.fr
*
E-mail: christian.robert@univ-lyon1.fr
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Abstract

We consider the class of concave distortion risk measures to study how choice is influenced by the decision-maker's attitude to risk and provide comparative statics results. We also assume ambiguity about the probability distribution of the risk and consider a framework à la Klibanoff, Marinacci and Mukerji (2005; A smooth model of decision making under ambiguity. Econometrica, 73, 1849–1892) to study the value of information that resolves ambiguity. We show that this value increases with greater ambiguity, with greater ambiguity aversion, and in some cases with greater risk aversion. Finally, we examine whether a more risk-averse and a more ambiguity-averse individual will invest in more effort to shift his initial risk distribution to a better target distribution.

Keywords

Ambiguityambiguity aversioncomparative statics resultsdistortion risk measuresrisk aversion
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 2 , May 2014 , pp. 277 - 302
Copyright
Copyright © ASTIN Bulletin 2014 

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References

Acerbi, C. (2002) Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking and Finance, 26 (7), 1505–1518.CrossRefGoogle Scholar
Alary, D., Gollier, C. and Treich, N. (2013) The effect of ambiguity aversion on insurance and self-protection. The Economic Journal, 123, 1188–1202.Google Scholar
Artzner, P., Delbaen, F., Eber, J.M. and Heath, D. (1999) Coherent measures of risk. Mathematical Finance, 9, 203–228.Google Scholar
Bignozzi, V. and Tsanakas, A. (2013) Residual estimation risk. Working paper Cass Business School, City University of London.Google Scholar
Cairns, A. (2000) A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics, 27 (3), 313–330.Google Scholar
Denneberg, D. (1990) Distorted probabilities and insurance premiums. Methods of Operations Research, 63, 3–5.Google Scholar
Denuit, M., Kaas, R., Goovaerts, M. and Dhaene, J. (2005) Actuarial Theory for Dependent Risks: Measures, Orders and Models. New York: Wiley.Google Scholar
Dhaene, J.L.M., Vanduffel, S., Goovaerts, M.J., Kaas, R., Tang, Q. and Vyncke, D. (2006) Risk measures and comonotonicity: A review. Stochastic Models, 22 (4), 573–606.Google Scholar
Diamond, P.A. and Stiglitz, J.E. (1974) Increases in risk and risk aversion. Journal of Economic Theory, 8, 337–360.Google Scholar
Doherty, N. and Eeckhoudt, L. (1995) Optimal insurance without expected utility: The dual theory and the linearity of insurance contracts. Journal of Risk and Uncertainty, 10, 157–179.CrossRefGoogle Scholar
Eeckhoudt, L., Godfroid, P. and Gollier, C. (1997) Willingness to pay, the risk premium and risk aversion. Economics Letters, 55 (3), 355–360.Google Scholar
Ellsberg, D. (1961) Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics, 75, 643–669.CrossRefGoogle Scholar
Etner, J., Jeleva, M. and Tallon, J.-M. (2012) Decision theory under ambiguity. Journal of Economic Surveys, 26 (2), 234–270.Google Scholar
Hammond, J.S. (1974) Simplifying the choice between uncertain prospects where preference is nonlinear. Management Science, 20 (7), 1047–1072.Google Scholar
Huang, R.J. (2012) Ambiguity aversion, higher-order risk attitude and optimal effort. Insurance: Mathematics and Economics, 50 (3), 338–345.Google Scholar
Jewitt, I. (1989) Choosing between risky prospects: The characterization of comparative statics results, and location independent risk. Management Science, 35 (1), 60–70.Google Scholar
Klibanoff, P., Marinacci, M. and Mukerji, S. (2005) A smooth model of decision making under ambiguity. Econometrica, 73, 1849–1892.Google Scholar
Laeven, R.J.A. and Goovaerts, M.J. (2011) Premium Calculation and Insurance Pricing. Working paper. Encyclopedia of Quantitative Risk Analysis and Assessment. http://onlinelibrary.wiley.com/doi/10.1002/9780470061596.risk0364/abstractGoogle Scholar
Landsman, Z. and Tsanakas, A. (2012) Parameter uncertainty in exponential family tail estimation. ASTIN Bulletin, 42 (1), 123–152.Google Scholar
Montesano, A. (1990) On the definition of risk aversion. Theory and Decision, 29, 53–68.CrossRefGoogle Scholar
Röell, A. (1987) Risk aversion in Quiggin and Yaari's rank-order model of choice under uncertainty. The Economic Journal, 97, 143–159.Google Scholar
Ross, S.A. (1981) Some stronger measures of risk aversion in the small and in the large with applications. Econometrica, 49, 621–663.Google Scholar
Snow, A. (2010) Ambiguity and the value of Information. Journal of Risk and Uncertainty, 40, 133–145.Google Scholar
Snow, A. (2011) Ambiguity aversion and the propensities for self-insurance and self-protection. Journal of Risk and Uncertainty, 42, 27–43.Google Scholar
Tsanakas, A. and Christofides, N. (2006) Risk exchange with distorted probabilities. ASTIN Bulletin, 36 (1), 219–243.Google Scholar
Tsanakas, A. and Desli, E. (2003) Risk measures and theories of choice. British Actuarial Journal, 9 (4), 959–991.Google Scholar
Wang, S. (1996) Premium calculation by transforming the layer premium density. ASTIN Bulletin, 26, 71–92.Google Scholar
Wang, S. (2000) A class of distortion operators for pricing financial and insurance. Journal of Risk and Insurance, 67 (1), 15–36.Google Scholar
Wang, S. and Young, V. (1998) Ordering of risks: Expected utility theory versus Yaari's dual theory of risk. Insurance: Mathematics and Economics, 22, 145–161.Google Scholar
Yaari, M.E. (1987) The dual theory of choice under risk. Econometrica, 55, 95–115.CrossRefGoogle Scholar