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Blätter der DGVFM

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

Additivity and premium calculation principles

  • B. Heijnen
  • M. J. Goovaerts
Article
  • 33 Downloads

Zusammenfassung

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.

Summary

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.

Keywords

Power Series Variance Principle Additive Mapping Additive Principle Constant Risk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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