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On convex principles of premium calculation. (English) Zbl 0579.62090

Related to the doctoral dissertation of the first author the paper introduces the concept of a convex premium calculation principle and discusses a variety of properties related to this.
If premiums are calculated according to convex principles, the authors consider the problem of optimal cooperation. They give general solutions which generalize the results of H. Bühlmann, Mathematical methods in risk theory. (1970; Zbl 0209.233) and H. U. Gerber, An introduction to mathematical risk theory. (1980; Zbl 0431.62066).
Reviewer: A.Reich

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:

[1] Bühlmann, H., Mathematical methods in risk theory, (1970), Springer New York-Heidelberg-Berlin · Zbl 0209.23302
[2] Bühlmann, H., An economic premium principle, Astin bulletin, 11, 52-60, (1980)
[3] Deprez, O., Konvexe prämienberechnungsprinzipien, ()
[4] Ekeland, I.; Temam, R., Convex analysis and variational problems, (1976), North-Holland Amsterdam-New York
[5] Gerber, H.U., An introduction to mathematical risk theory, (1980), The S.S. Huebner Foundation Philadelphia, PA, distributed by Irwin, Homewood, IL.
[6] Gerber, H.U., The esscher premium principle: A criticism, Astin bulletin, 12, 139-140, (1981)
[7] Goovaerts, M.J.; De Vylder, F.; Haezendonck, J., Insurance premiums, (1984), North-Holland Amsterdam-New York · Zbl 0532.62082
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