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Matrix calculation for ultimate and 1-year risk in the Semi-Markov individual loss reserving model

Author

Listed:
  • Bettonville, Carole
  • d'Oultremont, Louise
  • Denuit, Michel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Trufin, Julien
  • Van Oirbeek, Robin

Abstract

This paper proposes a multistate model with a Semi-Markov dependence structure describing the different stages in the settlement process of individual claims in general insurance. Every trajectory, from reporting to closure is combined with a modeling of individual link ratios to obtain the ultimate cost of each claim. Analytical expressions are derived for the moments of ultimate amounts whereas quantile risk measures can be obtained by simulation. In the 1-year view, the proposed matrix calculations avoid the simulation-within-simulation issue and offer a tractable evaluation method. A case study illustrates the relevance of the proposed approach.

Suggested Citation

  • Bettonville, Carole & d'Oultremont, Louise & Denuit, Michel & Trufin, Julien & Van Oirbeek, Robin, 2021. "Matrix calculation for ultimate and 1-year risk in the Semi-Markov individual loss reserving model," LIDAM Reprints ISBA 2021017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2021017
    DOI: https://doi.org/10.1080/03461238.2020.1848912
    Note: In: Scandinavian Actuarial Journal, Vol. 2021, no.5, p. 380-407 (2021)
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