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The Exponential Premium Calculation Principle Revisited

Published online by Cambridge University Press:  29 August 2014

Michel Denuit
Michel Denuit*
Affiliation:
Université Libre de Bruxelles, Bruxelles, Belgium
*
Institut de Statistique et de Recherche Opérationnelle, Université Libre de Bruxelles, Campus de la Plaine, CP 210, B-1050 Bruxelles, Belgium
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Abstract

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In this paper, it is shown how to approximate theoretical premium calculation principles in order to make them useful in practice. The method relies on stochastic extrema in moment spaces and is illustrated with the aid of the exponential principle.

Keywords

Premium Calculation PrinciplesMoment Spaces5-Convex OrderingsStochastic Extrema
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 29 , Issue 2 , November 1999 , pp. 215 - 226
Copyright
Copyright © International Actuarial Association 1999

References

Denuit, M., De Vylder, F.E., and Lefèvre, Cl. (1999). Extremal generators and extremal distributions for the continuous s-convex stochastic orderings. Insurance: Mathematics and Economics, to appear.Google Scholar
Denuit, M., and Lefèvre, Cl. (1997). Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences. Insurance: Mathematics and Economics 20, 20–197.Google Scholar
Denuit, M., Lefèvre, Cl., and Shared, M. (1998). The s-convex orders among real random variables, with applications. Mathematical Inequalities and Their Applications 1, 1–585.Google Scholar
De Vylder, F.E. (1996). Advanced Risk Theory. A Self-Contained Introduction. Editions de l'Université Libre de Bruxelles - Swiss Association of Actuaries, Bruxelles.Google Scholar
Goovaerts, M.J., de Vylder, F.E., and Haezendonck, J. (1984). Insurance Premiums: Theory and Applications. North Holland. Amsterdam.Google Scholar
Goovaerts, M.J., Kaas, R., Vanheerwaarden, A.E., and Bauwelinckx, T. (1990). Effective Actuarial Methods. North Holland. Amsterdam.Google Scholar
Hürlimann, W. (1996). Improval analytical bounds for some risk quantities. ASTIN Bulletin. 26, 185–199.CrossRefGoogle Scholar
Kaas, R., and Hesselager, O. (1995). Ordering claim size distributions and mixed Poisson probabilities. Insurance: Mathematics and Economics 17, 17–193.Google Scholar
Kaas, R., Van Heerwaarden, A.E., and Goovaerts, M.J. (1994). Ordering of Actuarial Risks. CAIRE. Brussels.Google Scholar
Levy, H. (1992). Stochastic dominance and expected utility: survey and analysis. Management Sciences 38, 38–555.Google Scholar
Roberts, A.W., and Varberg, D.E. (1973). Convex Functions. Academic Press, New York.Google Scholar
Shared, M., and Shanthikumar, J.G. (1994). Stochastic Orders and their Applications. Academic Press. New York.Google Scholar
Silva, J.M.A., and Centeno, M.L. (1998). Comparing risk adjusted premiums from the reinsurance point of view. ASTIN Bulletin 28, 28–221.CrossRefGoogle Scholar
Wang, S. (1996). Premium calculation by transforming the layer premium density. ASTIN Bulletin 26, 26–71.CrossRefGoogle Scholar
Wang, S., and Young, V. (1998). Risk-adjusted credibility premiums using distorted probabilities. Scandinavian Actuarial Journal, 143–165.CrossRefGoogle Scholar