Optimal insurance design of ambiguous risks
Tóm tắt
We examine the characteristics of the optimal insurance contract under linear transaction costs and an ambiguous distribution of losses. Under the standard expected utility model, we know from Arrow (1965) that it contains a straight deductible. In this paper, we assume that the policyholder is ambiguity averse in the sense of Klibanoff et al. (Econometrica 73(6):1849–1892, 2005). The optimal contract depends upon the structure of the ambiguity. For example, if the set of possible priors can be ranked according to the monotone likelihood ratio order, the optimal contract contains a disappearing deductible. We also show that the policyholder’s ambiguity aversion may have the counterintuitive effect to reduce the optimal insurance coverage of an ambiguous risk.
Tài liệu tham khảo
Alary, D., Gollier, C., Treich, N.: The effect of ambiguity aversion on insurance and self-protection. Econ. J. 123, 1188–1202 (2013)
Arrow, K.J.: Uncertainty and the welfare economics of medical care. Am. Econ. Rev. 53, 941–973 (1963)
Arrow, K.J.: Yrjo Jahnsson Lecture Notes, Helsinki (1965). Reprinted in Arrow (1971)
Arrow, K.J.: Essays in the Theory of Risk Bearing. Markham Publishing, Chicago (1971)
Arrow, K.J.: Optimal insurance and generalized deductibles. Scand. Actuar. J. 1, 1–42 (1974)
Athey, S.C.: Monotone comparative statics under uncertainty. Q. J. Econ. 117(1), 187–223 (2002)
Blazenko, G.: The design of an optimal insurance policy: note. Am. Econ. Rev. 75, 253–255 (1985)
Carlier, G., Dana, R.A., Shahidi, N.: Efficient insurance contracts under epsilon-contaminated utilities. Geneva Risk Insur. Rev. 28(1), 59–71 (2003)
De Castro, L.I., Chateauneuf, A.: Ambiguity aversion and trade. Econ. Theory 48, 243–273 (2011)
Eeckhoudt, L., Gollier, C., Schlesinger, H.: Increase in risk and deductible insurance. J. Econ. Theory 55, 435–440 (1991)
Ellsberg, D.: Risk, ambiguity, and the savage axioms, Q. J. Econ. 75, 643–669 (1961)
Gilboa, I., Schmeidler, D.: Maximin expected utility with non-unique prior. J. Math. Econ. 18, 141–153 (1989)
Ghirardato, P., Maccheroni, F., Marinacci, M.: Differentiating ambiguity and ambiguity attitude. J. Econ. Theory 118, 133–173 (2004)
Gollier, C.: The Economics of Risk and Time. MIT Press, Cambridge (2001)
Gollier, C.: Does ambiguity aversion reinforce risk aversion? Applications to portfolio choice and asset pricing. Rev. Econ. Stud. 78(4), 1329–1344 (2011)
Gollier, C., Schlesinger, H.: Arrow’s theorem on the optimality of deductibles: a stochastic dominance approach. Econ. Theory 7, 359–363 (1996)
Huberman, G., Mayers, D., Smith, C.W.: Optimal insurance policy indemnity schedules. Bell J. Econ. 14, 415–426 (1983)
Iwaki, H., Osaki, Y.: The dual theory of smooth ambiguity model. Econ. Theory 56, 275–289 (2014)
Jewitt, I.: Risk aversion and the choice between risky prospects: the preservation of comparative statics results. Rev. Econ. Stud. 54, 73–85 (1987)
Ju, N., Miao, J.: Ambiguity, learning, and asset returns. Econometrica 80, 559–591 (2012)
Karlin, S.: Total Positivity. Stanford University Press, Stanford (1968)
Karni, E.: Optimal insurance: a nonexpected utility analysis. In: Dionne, G. (ed.) Contributions to Insurance Economics. Kluwer, Boston (1992)
Klibanoff, P., Marinacci, M., Mukerji, S.: A smooth model of decision making under ambiguity. Econometrica 73(6), 1849–1892 (2005)
Klibanoff, P., Marinacci, M., Mukerji, S.: Recursive smooth ambiguity preferences. J. Econ. Theory 144, 930–976 (2009)
Klibanoff, P., Marinacci, M., Mukerji, S.: Definitions of ambiguous events and the smooth ambiguity model. Econ. Theory 48, 399–424 (2011)
Liu, J.-T., Tsou, M.-W., Hammitt, J.K.: Health information and subjective survival probabilities: evidence from Taiwan. J. Risk Res. 10(2), 149–175 (2007)
Maccheroni, F., Marinacci, M., Ruffino, D.: Alpha as ambiguity: robust mean-variance portfolio analysis. Econometrica 81, 1075–1113 (2013)
Machina, M.: Non-expected utility and the robustness of the classical insurance paradigm. In: Gollier, C., Machina, M. (eds.), Non-Expected Utility and Risk Management. Kluwer, Boston (1995). reprinted from The Geneva Papers on Risk and Insurance Theory, 20, 9–50
Martínez-Correa, J.: Risk management and insurance decisions under ambiguity, unpublished paper. Georgia State University (2012)
Mossin, J.: Aspects of rational insurance purchasing. J. Polit. Econ. 76, 533–568 (1968)
Raviv, A.: The design of an optimal insurance policy. Am. Econ. Rev. 69, 84–96 (1979)
Rothschild, M., Stiglitz, J.: Increasing risk: I. A definition. J. Econ. Theory 2, 225–243 (1970)
Slovic, P.: The Perception of Risk. Earthscan Publications, London (2000)
Vergopoulos, V.: Dynamic consistency for non-expected utility preferences. Econ. Theory 48, 493–518 (2011)
Zilcha, I., Chew, S.H.: Invariance of the efficient sets when the expected utility hypothesis is relaxed. J. Econ. Behav. Organ. 13, 125–131 (1990)