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Additivity of Chain-Ladder Projections

Published online by Cambridge University Press:  29 August 2014

Björn Ajne
Björn Ajne*
Affiliation:
Skandia, Stockholm
*
Skandia, S-103 50 Stockhom
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Abstract

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In this paper some results are given on the addivity of chain-ladder projections. Given two claims development triangles, when do their chain-ladder projections add up to the projections of the combined triangle, that is the triangle being the element-wise sum of the two given triangles?

Necessary and sufficient conditions for equality are given. These are of a fairly simply form and are directly connected to the ordinary chain-ladder calculations. In addition, sufficient conditions of the same form are given for inequality between the combined projection vector and the sum of the two original projections vectors.

Keywords

Chain-ladder projections
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 24 , Issue 2 , November 1994 , pp. 311 - 318
Copyright
Copyright © International Actuarial Association 1994

References

Ajne, B. (1991) A Note on the Additivity of Chain-ladder Projections. Paper presented to the 23rd ASTIN Colloquium (Speaker's corner).Google Scholar
Andersson, K. (1992) A Direttissima in Chain-ladder and the Danger of Direttissimas. Personal communication.Google Scholar
Bühlmann, H. (1993) Claims Reserves: Theory and Practice. Mimeographed paper.Google Scholar
Mack, T. (1991) A Simple Parametric Model for Rating Automobile Insurance or Estimating IBNR Claims Reserves. ASTIN Bulletin 21, 93–109.CrossRefGoogle Scholar