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Premium Calculation by Transforming the Layer Premium Density

Published online by Cambridge University Press:  29 August 2014

Shaun Wang
Shaun Wang*
Affiliation:
University of Waterloo, Canada
*
Dept. of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada, E-mail: sswang@math.uwaterloo.ca
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Abstract

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This paper examines a class of premium functionals which are (i) comonotonic additive and (ii) stochastic dominance preservative. The representation for this class is a transformation of the decumulative distribution function. It has close connections with the recent developments in economic decision theory and non-additive measure theory. Among a few elementary members of this class, the proportional hazard transform seems to stand out as being most plausible for actuaries.

Keywords

Premium calculation principlecomonotonicitystochastic dominancemean-variance analysisproportional hazard transform
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 1 , May 1996 , pp. 71 - 92
Copyright
Copyright © International Actuarial Association 1996

References

REFERENCES

Albrecht, P. (1992). Premium calculation without arbitrage? A note on a contribution by G. Venter. ASTIN Bulletin, 22, 247–254.CrossRefGoogle Scholar
Allais, M. (1953). Le comportement de l'homme rationel devant le risque: critique des axioms et postulates de l'ecole Americaine. Econometrica 21(4), 503–46.CrossRefGoogle Scholar
Borch, K.H. (1961). The utility concept applied to the theory of insurance. ASTIN Bulletin, 1, 170–191.CrossRefGoogle Scholar
Buhlmann, H. (1980) An economic premium principle. ASTIN Bulletin, 11, 52–60.CrossRefGoogle Scholar
Denneberg, D. (1990). Premium calculation: why standard deviation should be replaced by absolute deviation. ASTIN Bulletin, 20: 181–190.CrossRefGoogle Scholar
Denneberg, D. (1994). Non-Addititue Measure And Integral. Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
Fishburn, P. (1982). The Foundations of Expected Utility. Reidel, Dordrecht, Holland.CrossRefGoogle Scholar
Freifelder, L.R. (1979). Exponential utility theory ratemaking: an alternative ratemaking approach. Journal of Risk and Insurance, 46: 515–530.CrossRefGoogle Scholar
Gerber, H.U. (1979). An Introduction to Mathematical Risk Theory. Huebner Foundation Monograph, Wharton School, University of Pennsylvania.Google Scholar
Goovaerts, M.J., de Vylder, F. and Haezendonck, J. (1984) Insurance Premiums: Theory and Applications. North-Holland, Amsterdam.Google Scholar
Kaas, R., Van Heerwaarden, A.E., and Goovaerts, M.J. (1994) Ordering of Actuarial Risks. Ceuterick, Leuven, Belgium.Google Scholar
Machina, M. (1982) ‘Expected Utility’ analysis without the independence axiom. Econometrica, 50(2), 217–323.CrossRefGoogle Scholar
Meyers, G.G. (1991). The competitive market equilibrium risk load formula for increased limits ratemaking. Proceedings of the Casualty Actuarial Society. Vol. LXXVIII, 163–200.Google Scholar
Quiggin, J. (1982). A theory of anticipated utility. Journal of Economic Behavior and Organization, 3(4), 323–43.CrossRefGoogle Scholar
Ramsay, C.M. (1994) Loading gross premiums for risk without using utility theory, with Discussions. Transactions of the Society of Actuaries. Vol. XLV, p. 305–349.Google Scholar
Reich, A. (1986) Properties of premium calculation principles. Insurance: Mathematics and Economics, 5, 97–101.Google Scholar
Robbin, , (1992). Discussion of Meyers' paper – The competitive market equilibrium risk load formula for increased limits ratemaking. Proceedings of the Casualty Actuarial Society. Vol. LXXIX, 367–384.Google Scholar
Rotschield, M. and Stiglitz, J.E. (1970) Increasing risk I: a definition. Journal fo Economic Theory 2, 225–243.CrossRefGoogle Scholar
Schmeidler, D. (1986). Integral representation without additivity. Proceedings of the American Mathematical Society, 97: 225–261.CrossRefGoogle Scholar
van Heerwaarden, A.E. and Kaas, R. (1992) The Dutch premium principle. Insurance: Mathematics and Economics, 11, 129–133.Google Scholar
Venter, G.G. (1991) Premium calculation inmplications of reinsurance without arbitrage. ASTIN Bulletin, 21, 223–230.CrossRefGoogle Scholar
Wang, S. (1995) Insurance Pricing And Increased Limits Ratemaking By Proportional Hazards Transforms. Insurance: Mathematics and Economics, 17, 43–54.Google Scholar
Yaari, M.E. (1987). The dual theory of choice under risk. Econometrica, 55: 95–115.CrossRefGoogle Scholar