par Denuit, Michel ;Trufin, Julien
Référence North American actuarial journal, 21, 4, page (611-619)
Publication Publié, 2017-12-06
Article révisé par les pairs
Résumé : This paper 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, that 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 into 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 approach proposed in this paper.