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Additivity of Chain-Ladder Projections

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  • Ajne, Björn

Abstract

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.

Suggested Citation

  • Ajne, Björn, 1994. "Additivity of Chain-Ladder Projections," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 311-318, November.
    • Handle: RePEc:cup:astinb:v:24:y:1994:i:02:p:311-318_00
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    Cited by:

    1. Avanzi, Benjamin & Taylor, Greg & Vu, Phuong Anh & Wong, Bernard, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 50-71.
    2. Klaus Schmidt, 2012. "Loss prediction based on run-off triangles," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 265-310, June.
    3. Benjamin Avanzi & Gregory Clive Taylor & Phuong Anh Vu & Bernard Wong, 2020. "A multivariate evolutionary generalised linear model framework with adaptive estimation for claims reserving," Papers 2004.06880, arXiv.org.
    4. Zhang, Yanwei, 2010. "A general multivariate chain ladder model," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 588-599, June.
    5. Yannick Appert-Raullin & Laurent Devineau & Hinarii Pichevin & Philippe Tann, 2013. "One-Year Volatility of Reserve Risk in a Multivariate Framework," Working Papers hal-00848492, HAL.
    6. Kris Peremans & Stefan Van Aelst & Tim Verdonck, 2018. "A Robust General Multivariate Chain Ladder Method," Risks, MDPI, vol. 6(4), pages 1-18, September.

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