Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T12:37:49.461Z Has data issue: false hasContentIssue false
  • English
  • Français

The Linear Markov Property in Credibility Theory

Published online by Cambridge University Press:  29 August 2014

Thomas Witting
Thomas Witting*
Affiliation:
ETH Zürich
*
ETH Zürich, Mathematikdepartement HG G 36.1, Rämistr. 101, CH-8092 Zürich.
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.

We study the linear Markov property, i.e. the possibility of basing the credibility estimator on data of the most recent time period without loss of accuracy. Necessary and sufficient conditions are derived generally. The meaning of the linear Markov property is also discussed in different experience rating and loss reserving models.

Keywords

Linear Markov propertylinear sufficiencycredibility
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 17 , Issue 1 , April 1987 , pp. 71 - 84
Copyright
Copyright © International Actuarial Association 1987

References

Bühlmann, H. and Jewell, W. S. (1986) Hierarchical credibility. Preprint for the Summer School 1986 of the Association of Swiss Actuaries.Google Scholar
Bühlmann, H. and Straub, E. (1970) Glaubwürdigkeit für Schadensätze. Bulletin of the Association of Swiss Actuaries 70/1, 111–133.Google Scholar
De Vylder, F. (1982) Estimation of IBNR-claims by credibility theory. Insurance: Mathematics and Economics 82/1, 21–45.Google Scholar
Drygas, H. (1983) Sufficiency and completeness in the general Gauss–Markov model. Sankhya A 45, 88–98.Google Scholar
Drygas, H. (1985) Linear sufficiency and some applications in multilinear estimation. Journal of Multivariate Analysis 16, 71–84.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability and its Applications, Vol. 2. Wiley, New York.Google Scholar
Jewell, W. S. (1975) Two classes of covariance matrices giving simple linear forecasts. IIASA Research Memorandum 75/17.Google Scholar
Kramreiter, H. and Straub, E. (1973) On the calculation of IBNR reserves II. Bulletin of the Association of Swiss Actuaries 73, 177–190.Google Scholar
Neuhaus, W. (1985) Choice of statistics in linear Bayes estimation. Scandinavian Actuarial Journal 85/1, 1–26.CrossRefGoogle Scholar
Norberg, R. (1985) A contribution to modelling of IBNR claims. Statistical Research Report of the University of Oslo 85/4.Google Scholar
Papoulis, A. (1965) Probability, Random Variables and Stochastic Processes. McGraw-Hill, Tokyo.Google Scholar
Shur, W. (1972) Discussion of Margolin's “Credibility of group insurance claim experience”. Transactions of the Society of Actuaries 23, 240–251.Google Scholar
Sundt, B. (1979) Credibility and relative exchangeability. Scandinavian Actuarial Journal 79, 45–51.CrossRefGoogle Scholar
Witting, T. (1986) Über Kredibilitätsschätzungen von reinen IBNR-Schäden. Dissertation ETH Nr. 8042.Google Scholar