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AN ECONOMIC PREMIUM PRINCIPLE UNDER THE DUAL THEORY OF THE SMOOTH AMBIGUITY MODEL

Published online by Cambridge University Press:  30 May 2017

Yoichiro Fujii ,
Hideki Iwaki  and
Yusuke Osaki
Yoichiro Fujii
Affiliation:
Faculty of Economics, Osaka Sangyo University, Osaka, Japan, E-Mail: [email protected]
Hideki Iwaki*
Affiliation:
Faculty of Business Administration, Kyoto Sangyo University, Kyoto, Japan
Yusuke Osaki
Affiliation:
Faculty of Economics, Osaka Sangyo University, Osaka, Japan, E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

This study considers a pure exchange economy with insurance against ambiguous loss. Ambiguity preferences are represented by the dual theory of the smooth ambiguity model from Iwaki and Osaki (2014). The economic premium principle of Bühlmann (1980, 1984) is extended to ambiguity. We also perform some comparative statics and present sufficient conditions under which an increase in ambiguity aversion increases insurance demand and insurance premiums. Contrary to the result in Tsanakas and Christofides (2006), the optimal demand for insurance is not always comonotonic, because our model permits an economy comprising both ambiguity averse and ambiguity loving agents.

Keywords

Ambiguityeconomic premium principleequilibriumthe dual theory of the smooth ambiguity model
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 47 , Issue 3 , September 2017 , pp. 787 - 801
Copyright
Copyright © Astin Bulletin 2017 

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References

Alary, D., Gollier, C. and Treich, N. (2013) The effect of ambiguity aversion on insurance and self-protection. The Economic Journal, 123, 1188–1202.CrossRefGoogle Scholar
Anwar, S. and Zheng, M. (2012) Competitive insurance market in the presence of ambiguity. Insurance: Mathematics and Economics, 50, 79–84.Google Scholar
Boonen, T. (2015) Competitive equilibria with distortion risk measures. Astin Bulletin, 45, 703–728.CrossRefGoogle Scholar
Bühlmann, H. (1980) An economic premium principle. Astin Bulletin, 11, 52–60.CrossRefGoogle Scholar
Bühlmann, H. (1984) The general economic premium principle. Astin Bulletin, 14, 13–21.CrossRefGoogle Scholar
Carlier, G. and Dana, R. (2013) Pareto optima and equilibria when preferences are incompletely known. Journal of Economic Theory, 148, 1606–1623.CrossRefGoogle Scholar
Cerreia-Vioglio, S., Maccheroni, F., Marinacci, M. and Montrucchio, L. (2013) Ambiguity and robust statistics. Journal of Economic Theory, 148, 974–1049.CrossRefGoogle Scholar
Chateauneuf, A., Dana, R. and Tallon, J. (2000) Optimal risk-sharing rules and equlibria with Choquet-expected-utility. Journal of Mathematical Economics, 34, 191–214.CrossRefGoogle Scholar
Chiu, H., Eeckhoudt, L. and Rey, B. (2012) On relative and partial risk attitudes: Theory and implications. Economic Theory, 50, 151–167.CrossRefGoogle Scholar
de Castro, L. and Chateauneuf, A. (2011) Ambiguity aversion and trade. Economic Theory, 48, 243–273.CrossRefGoogle Scholar
Eeckhoudt, L. and Schlesinger, H. (2006) Putting risk in its proper place. American Economic Review, 96, 280–289.CrossRefGoogle Scholar
Ellsberg, D. (1961) Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75, 643–669.CrossRefGoogle Scholar
Fishburn, P.C. and Porter, B. (1976) Optimal portfolio with one safe and one risky asset: Effects of changes in rate of return and risk. Management Science, 22, 1064–1073.CrossRefGoogle Scholar
Gilboa, I. and Schmeidler, D. (1989) Maxmin expected utility with non-unique prior. Journal of Mathematical Economics, 18, 141–153.CrossRefGoogle Scholar
Gollier, C. (2001) The Economics of Risk and Time. Cambridge: The MIT Press.CrossRefGoogle Scholar
Gollier, C. (2014) Optimal insurance design of ambiguous risks. Economic Theory, 57, 555–576.CrossRefGoogle Scholar
Huang, R. (2012) Ambiguity aversion, higher-order risk attitude and optimal effort. Insurance: Mathematics and Economics, 50, 338–345.Google Scholar
Iwaki, H. and Osaki, Y. (2014) The dual theory of the smooth ambiguity model. Economic Theory, 56, 275–289.CrossRefGoogle Scholar
Karatzas, I. and Shreve, S. (1998) Methods of Mathematical Finance. New York: Springer-Verlag.Google Scholar
Klibanoff, P., Marinacci, M. and Mukerji, S. (2005) A smooth model of decision making under ambiguity. Econometrica, 58, 1849–1892.CrossRefGoogle Scholar
Kocher, M. G., Lahno, A. M. and Trautmann, S. T. (2015) Ambiguity aversion is the exception. Munich Discussion Paper 2015-2. Available at https://epub.ub.uni-muenchen.de/23817/ CrossRefGoogle Scholar
Robert, C. and Thérond, P.-E. (2014) Distortion risk measures, ambiguity aversion and optimal effort. Astin Bulletin, 44, 277–302.CrossRefGoogle Scholar
Sarin, R. and Weber, M. (1993) Effects of ambiguity in market experiments. Management Science, 39, 602–615.CrossRefGoogle Scholar
Schmeidler, D. (1989) Subjective probability and expected utility without additivity. Econometrica, 57, 571–587.CrossRefGoogle Scholar
Segal, U. (1987) The Ellsberg paradox and risk aversion: An anticipated utility approach. International Economic Review, 28, 175–202.CrossRefGoogle Scholar
Snow, A. (2011) Ambiguity aversion and the propensities for self-insurance and self-protection. Journal of Risk and Uncertainty, 42, 27–43.CrossRefGoogle Scholar
Tsanakas, A. and Christofides, N. (2006) Risk exchange with distorted probabilities. Astin Bulletin, 36, 219–243.CrossRefGoogle Scholar
Viscusi, W. and Chesson, H. (1999) Hopes and fears: The conflicting effects of risk ambiguity. Theory and Decision, 47, 153–178.CrossRefGoogle Scholar