Prague Economic Papers 2017, 26(4):450-466 | DOI: 10.18267/j.pep.621

Calculation of Solvency Capital Requirements for Non-life Underwriting Risk Using Generalized Linear Models

Jiří Valecký
Faculty of Economics, Department of Finance, VŠB-TU Ostrava, Czech Republic (jiri.valecky@vsb.cz)

The paper presents various GLM models using individual rating factors to calculate the solvency capital requirements for non-life underwriting risk in insurance. First, we consider the potential heterogeneity of claim frequency and the occurrence of large claims in the models. Second, we analyse how the distribution of frequency and severity varies depending on the modelling approach and examine how they are projected into SCR estimates according to the Solvency II Directive. In addition, we show that neglecting of large claims is as consequential as neglecting the heterogeneity of claim frequency. The claim frequency and severity are managed using generalized linear models, that is, negative-binomial and gamma regression. However, the different individual probabilities of large claims are represented by the binomial model and the large claim severity is managed using generalized Pareto distribution. The results are obtained and compared using the simulation of frequency-severity of an actual insurance portfolio.

Keywords: claim frequency, claim severity, generalized linear models, motor insurance, non-life insurance, solvency capital requirements, Solvency II, underwriting risk
JEL classification: C31, C58, G22

Published: August 1, 2017  Show citation

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Valecký, J. (2017). Calculation of Solvency Capital Requirements for Non-life Underwriting Risk Using Generalized Linear Models. Prague Economic Papers, 26(4), 450-466. doi: 10.18267/j.pep.621
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