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Beyond the Tweedie Reserving Model: The Collective Approach to Loss Development

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  • Michel Denuit
  • Julien Trufin

Abstract

This article proposes a new loss reserving approach, inspired from the collective model of risk theory. According to the collective paradigm, we do not relate payments to specific claims or policies, but we work within a frequency-severity setting, with a number of payments in every cell of the run-off triangle, together with the corresponding paid amounts. Compared to the Tweedie reserving model, which can be seen as a compound sum with Poisson-distributed number of terms and Gamma-distributed summands, we allow here for more general severity distributions, typically mixture models combining a light-tailed component with a heavier-tailed one, including inflation effects. The severity model is fitted to individual observations and not to aggregated data displayed in run-off triangles with a single value in every cell. In that respect, the modeling approach appears to be a powerful alternative to both the crude traditional aggregated approach based on triangles and the extremely detailed individual reserving approach developing each and every claim separately. A case study based on a motor third-party liability insurance portfolio observed over 2004–2014 is used to illustrate the relevance of the proposed approach.

Suggested Citation

  • Michel Denuit & Julien Trufin, 2017. "Beyond the Tweedie Reserving Model: The Collective Approach to Loss Development," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(4), pages 611-619, October.
  • Handle: RePEc:taf:uaajxx:v:21:y:2017:i:4:p:611-619
    DOI: 10.1080/10920277.2017.1353428
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    Cited by:

    1. N. Miklós Arató & László Martinek, 2022. "The Quality of Reserve Risk Calculation Models under Solvency II and IFRS 17," Risks, MDPI, vol. 10(11), pages 1-13, October.
    2. Crevecoeur, Jonas & Robben, Jens & Antonio, Katrien, 2022. "A hierarchical reserving model for reported non-life insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 158-184.
    3. Yanez, Juan Sebastian & Pigeon, Mathieu, 2021. "Micro-level parametric duration-frequency-severity modeling for outstanding claim payments," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 106-119.

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