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

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

Scandinavian Actuarial Journal, 2021, vol. 2021, issue 5, 380-407

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.

Date: 2021
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DOI: 10.1080/03461238.2020.1848912

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