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  • Christian Y. Robert (a1) and Pierre-E. Therond (a2)

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.

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Acerbi C. (2002) Spectral measures of risk: A coherent representation of subjective risk aversion. Journal of Banking and Finance, 26 (7), 15051518.
Alary D., Gollier C. and Treich N. (2013) The effect of ambiguity aversion on insurance and self-protection. The Economic Journal, 123, 11881202.
Artzner P., Delbaen F., Eber J.M. and Heath D. (1999) Coherent measures of risk. Mathematical Finance, 9, 203228.
Bignozzi V. and Tsanakas A. (2013) Residual estimation risk. Working paper Cass Business School, City University of London.
Cairns A. (2000) A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics, 27 (3), 313330.
Denneberg D. (1990) Distorted probabilities and insurance premiums. Methods of Operations Research, 63, 35.
Denuit M., Kaas R., Goovaerts M. and Dhaene J. (2005) Actuarial Theory for Dependent Risks: Measures, Orders and Models. New York: Wiley.
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), 573606.
Diamond P.A. and Stiglitz J.E. (1974) Increases in risk and risk aversion. Journal of Economic Theory, 8, 337360.
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, 157179.
Eeckhoudt L., Godfroid P. and Gollier C. (1997) Willingness to pay, the risk premium and risk aversion. Economics Letters, 55 (3), 355360.
Ellsberg D. (1961) Risk, ambiguity, and the savage axioms. Quarterly Journal of Economics, 75, 643669.
Etner J., Jeleva M. and Tallon J.-M. (2012) Decision theory under ambiguity. Journal of Economic Surveys, 26 (2), 234270.
Hammond J.S. (1974) Simplifying the choice between uncertain prospects where preference is nonlinear. Management Science, 20 (7), 10471072.
Huang R.J. (2012) Ambiguity aversion, higher-order risk attitude and optimal effort. Insurance: Mathematics and Economics, 50 (3), 338345.
Jewitt I. (1989) Choosing between risky prospects: The characterization of comparative statics results, and location independent risk. Management Science, 35 (1), 6070.
Klibanoff P., Marinacci M. and Mukerji S. (2005) A smooth model of decision making under ambiguity. Econometrica, 73, 18491892.
Laeven R.J.A. and Goovaerts M.J. (2011) Premium Calculation and Insurance Pricing. Working paper. Encyclopedia of Quantitative Risk Analysis and Assessment.
Landsman Z. and Tsanakas A. (2012) Parameter uncertainty in exponential family tail estimation. ASTIN Bulletin, 42 (1), 123152.
Montesano A. (1990) On the definition of risk aversion. Theory and Decision, 29, 5368.
Röell A. (1987) Risk aversion in Quiggin and Yaari's rank-order model of choice under uncertainty. The Economic Journal, 97, 143159.
Ross S.A. (1981) Some stronger measures of risk aversion in the small and in the large with applications. Econometrica, 49, 621663.
Snow A. (2010) Ambiguity and the value of Information. Journal of Risk and Uncertainty, 40, 133145.
Snow A. (2011) Ambiguity aversion and the propensities for self-insurance and self-protection. Journal of Risk and Uncertainty, 42, 2743.
Tsanakas A. and Christofides N. (2006) Risk exchange with distorted probabilities. ASTIN Bulletin, 36 (1), 219243.
Tsanakas A. and Desli E. (2003) Risk measures and theories of choice. British Actuarial Journal, 9 (4), 959991.
Wang S. (1996) Premium calculation by transforming the layer premium density. ASTIN Bulletin, 26, 7192.
Wang S. (2000) A class of distortion operators for pricing financial and insurance. Journal of Risk and Insurance, 67 (1), 1536.
Wang S. and Young V. (1998) Ordering of risks: Expected utility theory versus Yaari's dual theory of risk. Insurance: Mathematics and Economics, 22, 145161.
Yaari M.E. (1987) The dual theory of choice under risk. Econometrica, 55, 95115.
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ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
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