Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-24T01:18:33.002Z Has data issue: false hasContentIssue false
  • English
  • Français

Convergence of Bayes and Credibility Premiums

Published online by Cambridge University Press:  29 August 2014

Klaus D. Schmidt
Klaus D. Schmidt*
Affiliation:
University of Mannheim, West Germany
*
Fakultät für Mathematik und Informatik, Universität Mannheim, A 5, 6800 Mannheim, West Germany.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For a risk whose annual claim amounts are conditionally i.i.d. with respect to a risk parameter, it is known that the Bayes and credibility premiums are asymptotically optimal in terms of losses. In the present note it is shown that the Bayes and credibility premiums actually converge to the individual premium.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 20 , Issue 2 , November 1990 , pp. 167 - 172
Copyright
Copyright © International Actuarial Association 1990

References

Bauer, H. (1978) Wahrscheinlichkeitstheorie und Grundzüge der Maßtheorie, 3. Auflage. DeGruyter, Berlin-New York.CrossRefGoogle Scholar
Billingsley, P. (1986) Probability and Measure, Second Edition. Wiley, New York-Chichester.Google Scholar
Brockwell, P.J. and Davis, R.A. (1987) Time Series: Theory and Methods. Springer, Berlin-Heidelberg-New York.CrossRefGoogle Scholar
Bühlmann, H. (1967) Experience rating and credibility. ASTIN Bulletin 4, 199–207.CrossRefGoogle Scholar
Bühlmann, H. (1970) Mathematical Methods in Risk Theory. Springer, Berlin-Heidelberg-New York.Google Scholar
De Vylder, F. (1976) Geometrical credibility. Scandinavian Actuarial Journal, 121–149.CrossRefGoogle Scholar
Jewell, W. S. (1976) A survey of credibility theory. Operations Research Center Report No. 76-31. University of California, Department of Industrial Engineering and Operations Research, Berkeley.Google Scholar
Neveu, J. (1972) Martingales à Temps Discret. Masson, Paris.Google Scholar
Norberg, R. (1979) The credibility approach to experience rating. Scandinavian Actuarial Journal, 181–221.CrossRefGoogle Scholar
Schmidt, K. D. (1990) Conditional laws of large numbers and applications. Preprint.Google Scholar