Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T21:15:29.998Z Has data issue: false hasContentIssue false
  • English
  • Français

Insurance Premium Calculations with Anticipated Utility Theory

Published online by Cambridge University Press:  29 August 2014

Cuncun Luan
Cuncun Luan*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, China
*
Cuncun Luan Department of Mathematics, Nanjing University, Nanjing 210093, P.R., China, Email:[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper examines an insurance or risk premium calculation method called the mean-value-distortion pricing principle in the general framework of anticipated utility theory. Then the relationship between comonotonicity and independence is explored. Two types of risk aversion and optimal reinsurance contracts are also discussed in the context of the pricing principle.

Keywords

Mean-value-distortion pricing principleanticipated utility theorycomonotonicityrisk aversionand optimal reinsurance
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 1 , May 2001 , pp. 23 - 35
Copyright
Copyright © International Actuarial Association 2001

References

Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer-Verlag.Google Scholar
Chateauneuf, A., Cohen, M. and Meilijson, I. (1997) Comonotonicity, rank-dependent utilities and a search problem. In: Benes, V. and Stepan, J. (Ed.). Distributions with given marginals and moment problems. Kluwer Academic Publishers, Amsterdam.Google Scholar
Denneberg, D. (1994) Non-Additive Measure and Integral. Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
Denuit, M., Dhaene, J. and Van Wouve, M. (1999) The Economics of Insurance: a review and some recent developments. Bulletin of the Swiss Association of Actuaries, 137–175.Google Scholar
Goovaerts, M.J., De Vylder, F. and Haezendonck, J. (1984) Insurance Premiums: Theory and Applications. North-Holland, Amsterdam.Google Scholar
Goovaerts, M.J., Kaas, R., Van Heerwaarden, A.E. and Bavwelinck, X.T. (1990) Effective Actuarial Methods. North-Holland, Amsterdam.Google Scholar
Hürlimann, W. (1997) On quasi-mean value principles. Blätter der Deutschen Gesellschaft für Versicherungsmathematik XXIII, 1–16.Google Scholar
HüRlimann, W. (1998) On stop-loss order and the distortion pricing principles. ASTIN Bulletin 28(2), 119–134.CrossRefGoogle Scholar
Puppe, C. (1991) Distorted Probabilities and Choice under Risk. Springer-Verlag.CrossRefGoogle Scholar
Quiggin, J. (1982) A theory of anticipated utility. Journal of Economic Behavior and Organization 3, 323–343.CrossRefGoogle Scholar
Rothschild, M. and Stiglitz, J.E. (1970) Increasing risk: I. A Definition. Journal of Economic Theory 2, 225–243.CrossRefGoogle Scholar
Segal, U. (1989) Anticipated utility theory: a measure representation approach. Annals of Operations Research 19, 359–373.CrossRefGoogle Scholar
Schmeidler, D. (1986) Integral representation without additivity. Proceedings of American Mathematical Society 97, 255–261.CrossRefGoogle Scholar
Wang, S. (1996) Premium calculation by transforming the layer premium density. ASTIN Bulletin 26(2), 71–92.CrossRefGoogle Scholar
Wang, S., Young, V.R. and Panjer, H.H. (1997) Axiomatic characterization of insurance prices. Insurance: Mathematics and Economics 21, 173–183.Google Scholar
Wang, S. (1998) An actuarial index of the right-tail risk. North American Actuarial Journal 2(2), 89–101.CrossRefGoogle Scholar
Wang, S. and Young, V.R. (1998) Ordering of risks: utility theory verse 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
Young, V.R. (1998) Families of updated rules for non-additive measures: Applications in pricing risks. Insurance: Mathematics and Economics 23, 1–14.Google Scholar
Young, V.R. (1999) Optimal insurance under Wang's premium principle. Insurance: Mathematics and Economics 25, 109–122.Google Scholar