Blätter der DGVFM

, Volume 17, Issue 3, pp 217–223 | Cite as

Additivity and premium calculation principles

  • B. Heijnen
  • M. J. Goovaerts


Diese Arbeit zeigt, da\ das Erwartungswertprinzip die einzige Mischung von Esscher-Prinzipien ist, die auch ein Summationsprinzip ist. Au\erdem wird gezeigt, da\ das Varianz-Prinzip das einzige Covarianz-additive Prinzip zur PrÄmienkalkulation ist.


In this note it is shown that the expected value principle is the only mixture of Esscher principles that is also a cumulant principle. Secondly the variance principle is shown to be the only covariance-additive premium principle.


Power Series Variance Principle Additive Mapping Additive Principle Constant Risk 
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  1. [1]
    Gerber, H. U. andGoovaerts, M. J.: On the representation of additive principles of premium calculation. S.A. J. (1981), pp. 221–227.Google Scholar
  2. [2]
    Goovaerts, M. J., Vylder, F. De andHaezendonck, J.: Insurance premiums (eds.) (1984), North-Holland, pp. XI + 406.Google Scholar
  3. [3]
    Borch, K.: The safety loading of reinsurance premiums. S.A.J. (1960), pp. 163–184.Google Scholar
  4. [4]
    Borch, K.: Equilibrium in a reinsurance market. Econometrica (1962), pp. 424–444.Google Scholar
  5. [5]
    Borch, K.: A contribution to the theory of reinsurance markets. S.A.J. (1962), pp. 176–189.Google Scholar
  6. [6]
    RÄtz, J.: On orthogonally additive mappings. Aequationes Mathematicae (1985), to appear.Google Scholar

Copyright information

© DAV/DGVFM 1986

Authors and Affiliations

  • B. Heijnen
    • 1
  • M. J. Goovaerts
    • 2
  1. 1.Antwerpen
  2. 2.Leuven

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