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Inflation in reserving triangles : Taylor and Verbeek techniques are equivalent to a Chain Ladder on a calendar triangle

Author

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  • Sébastien Farkas

    (Allianz, Addia)

  • Amélie Roux

    (Allianz, ISUP - Institut de Statistique de Sorbonne Université - SU - Sorbonne Université, SU - Sorbonne Université)

Abstract

In this paper, we study the estimation of past inflation based on reserving triangles of average claims costs. More precisely, we focus on methodologies introduced by H. G. Verbeek in 1972 and by G.C. Taylor in 1977 that allows to estimate such an historical inflation index based on average claims costs triangle. Those methods rely on recursive formula that challenges the understanding of underlying assumptions and that can complexify the interpretation of the results. We alternatively show the equivalence of those techniques with a Chain Ladder on a specificly rearranged triangle. We therefore highligths the spirit of that technics that firstly compute the ultimate average claims costs by calendar year and secondly deduce the inflation index based on calendar evolutions. Moreover, this allow to rationalize the underlying assumptions of Taylor and Verbeek methodology, using the mathematical conceptualization of Chain Ladder by Mack in 1993. We illustrate those findings on simulated data.

Suggested Citation

  • Sébastien Farkas & Amélie Roux, 2024. "Inflation in reserving triangles : Taylor and Verbeek techniques are equivalent to a Chain Ladder on a calendar triangle," Working Papers hal-04019831, HAL.
    • Handle: RePEc:hal:wpaper:hal-04019831
    Note: View the original document on HAL open archive server: https://hal.science/hal-04019831v2
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    Keywords

    Actuarial science; Inflation; Chain Ladder; Taylor; Verbeek;
    All these keywords.

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