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

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  • Carole Bettonville
  • Louise d'Oultremont
  • Michel Denuit
  • Julien Trufin
  • Robin Van Oirbeek

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

  • Carole Bettonville & Louise d'Oultremont & Michel Denuit & Julien Trufin & Robin Van Oirbeek, 2021. "Matrix calculation for ultimate and 1-year risk in the Semi-Markov individual loss reserving model," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(5), pages 380-407, May.
    • Handle: RePEc:taf:sactxx:v:2021:y:2021:i:5:p:380-407
    DOI: 10.1080/03461238.2020.1848912
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