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Optimal Pricing of a Heterogeneous Portfolio for a Given Risk Level

Published online by Cambridge University Press:  17 April 2015

Yaniv Zaks ,
Esther Frostig  and
Benny Levikson
Yaniv Zaks
Affiliation:
Department of Statistics, University of Haifa, Israel
Esther Frostig
Affiliation:
Department of Statistics, University of Haifa, Israel
Benny Levikson
Affiliation:
Department of Statistics, University of Haifa, Israel
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Abstract

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Consider a portfolio containing heterogeneous risks, where the policyholders’ premiums to the insurance company might not cover the claim payments. This risk has to be taken into consideration in the premium pricing. On the other hand, the premium that the insureds pay has to be fair. This fairness is measured by the distance between the risk and the premium paid. We apply a non-linear programming formulation to find the optimal premium for each class so that the risk is below a given level and the weighted distance between the risk and the premium is minimized. We consider also the dual problem: minimizing the risk level for a given weighted distance between risks and premium.

Keywords

Heterogeneous portfolioPositive Definite Matrixnon-linear programmingdual problem
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 1 , May 2006 , pp. 161 - 185
Copyright
Copyright © ASTIN Bulletin 2006

Footnotes

1

This article is dedicated to the memory of our beloved friend Professor Benjamin Zeev Levikson who passed away on July, 16, 2005.

References

Baptiste, J., Urruty, H. and Lemarechal, C. (1993) Convex analysis and minimization algorithms I. Springer-Verlag, Berlin, Germany.Google Scholar
Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J. (1997) Actuarial Mathematics. The Society of Actuaries, U.S.A.Google Scholar
Censor, Y. and Reich, S. (1998) The Dykstra algorithm with Bregman projections, Communications in Applied Analysis, 2, 407–419.Google Scholar
Dykstra, R.L. (1983) An Algorithm for restricted least squares regression, Journal of American Statistical Association, 78, 837–842.CrossRefGoogle Scholar
Frangos, N.E. and Vrontos, S.D. (2001) Design of optimal Bonus-Malus Systems with a frequency and a severity component on an individual basis in automobile insurance. Astin Bulletin, 31(1), 5–26.CrossRefGoogle Scholar
Goovaerts, M.J., De Vylder, F. and Haezendonck, J. (1984) Insurance premiums. Elsevier Science Publishers B.V., Amsterdam, The Netherlands.Google Scholar
Kliger, D. and Levikson, B. (1998) Pricing Insurance contracts – An economic viewpoint. Insurance Mathematics and Economics, 22(3), 243–249.CrossRefGoogle Scholar
Lemaire, J. (1995) Bonus-Malus Systems in Automobile insurance. Kluwer Academic Publishers, Massachusetts, USA.Google Scholar