Tbilisi Mathematical Journal

Characterization theorems for mean value insurance premium calculation principle

Mykola Pratsiovytyi and Vitaliy Drozdenko

Full-text: Open access

Abstract

Characterization theorems for several properties possessed by the mean value insurance premium calculation principle are presented. Demonstrated theorems cover cases of additivity, consistency, iterativity, and scale invariance properties. Results are formulated in a form of necessary and sufficient conditions for attainment of the properties imposed on the auxiliary function with the help of which the mean value premium calculation principle is defined. We show also that for the mean value principle subjected to pricing of only strictly positive risks the class of the auxiliary functions producing scale invariant premiums is larger than in the general case.

Article information

Source
Tbilisi Math. J., Volume 6 (2013), 57-71.

Dates
Received: 9 August 2013
Revised: 11 December 2013
Accepted: 18 December 2013
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768937

Digital Object Identifier
doi:10.32513/tbilisi/1528768937

Mathematical Reviews number (MathSciNet)
MR3260492

Zentralblatt MATH identifier
1281.91102

Subjects
Primary: 91B30: Risk theory, insurance
Secondary: 62P20: Applications to economics [See also 91Bxx] 62P05: Applications to actuarial sciences and financial mathematics

Keywords
Characterization theorem insurance premium mean value premium principle additivity consistency iterativity scale invariance

Citation

Pratsiovytyi, Mykola; Drozdenko, Vitaliy. Characterization theorems for mean value insurance premium calculation principle. Tbilisi Math. J. 6 (2013), 57--71. doi:10.32513/tbilisi/1528768937. https://projecteuclid.org/euclid.tbilisi/1528768937


Export citation

References

  • S. Asmussen, H. Albrecher, Ruin Probabilities (second edition), World Sientific, Singapore, 2010.
  • P.J. Boland, Statistical and Probabilistic Methods in Actuarial Science, Chapman & Hall, Boca Raton, 2007.
  • N.L. Bowers, H.U. Gerber, J.C. Hickman, D.A. Jones, C.J. Nesbit, Actuarial Mathematics (second edition), The Society of Actuaries, Illinoice, 1997.
  • H. Bühlmann, Mathematical Methods in Risk Theory, Springer, Berlin, 1970.
  • D.C.M. Dickson, Insurance Risk and Ruin, Cambridge University Press, Cambridge, 2005.
  • H.U. Gerber, An Introduction to Mathematical Risk Theory, S. S. Huebner Foundation for Insurance Education, Philadelpia, 1979.
  • F.E. De Vylder, M. Goovaerts, J. Haezendonck (editors), Premium Calculation in Insurance (collection of articles), Kluwer Academic Publishers, Boston, 1984.
  • F.E. De Vylder, M. Goovaerts, J. Haezendonck (editors), Insurance and Risk Theory (collection of articles), Kluwer Academic Publishers, Boston, 1986.
  • R. Kaas, M. Goovaerts, J. Dhaene, M. Denuit, Modern Actuarial Risk Theory using R, Springer, Berlin, 2008.
  • E. Kremer, Applied Risk Theory, Shaker, Aachen, 1999.
  • T. Rolski, H. Schmidli, V. Schmidt, J. Teugels, Stochastic Processes for Insurance and Finance, John Wiley & Sons, Chichester, 1999.
  • E. Straub, Non-Life Insurance Mathematics, Springer, Berlin, 1988.