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A Note on Christofides' Conjecture Regarding Wang's Premium Principle1

Published online by Cambridge University Press:  29 August 2014

Wang Jing-Long
Wang Jing-Long*
Affiliation:
East China Normal University, Shanghai, China
*
Department of Statistics, East China Normal University, 3663 Zhongshan Road (Northern) Shanghai 200062, P.R., China
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Young (1999) discussed the conjecture proposed by Christofides (1998) regarding the premium principle of Wang (1995, 1996). She shows that this conjecture is true for location-scale families and for certain other families, but false in general. In addition Young (1999) states that it remains an open problem to determine under what circumstances Wang's premium principle reduces to the standard deviation (SD) premium principle.

In this paper we will provide further discussion of this problem. We will show that, for a fixed distortion, the natural set on which Wang's premium principle can reduce to the SD premium principle is and only is the union of location-scale families which satisfies some condition. Furthermore, it will be shown that the natural set is and only is a location-scale family if Wang's premium principle can be reduced to the SD premium principle for any distortion.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 30 , Issue 1 , May 2000 , pp. 13 - 17
Copyright
Copyright © International Actuarial Association 2000

Footnotes

1

Project 19831020 Supported by National Natural Science Foundation of China.

References

Christofides, S. (1998) Principle for risk in financial transactions. Proceedings of the GISG/ASTIN Joint Meeting in Glasgow, Scotland. October, 1998, 2, 63–109.Google Scholar
Wang, S.S. (1995) Insurance pricing and increased limits ratemaking by proportional hazards transforms. Insurance: Mathematics and Economics 17, 43–54.Google Scholar
Wang, S.S. (1996) Premium calculation by transforming the layer premium density. ASTIN Bulletin 26, 71–92.CrossRefGoogle Scholar
Young, V.R. (1999) Discussion of Christofides' conjecture regarding Wang's premium principle. ASTIN Bulletin 29, 191–195.CrossRefGoogle Scholar