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

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  • Jiří Valecký

Abstract

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.

Suggested Citation

  • Jiří Valecký, 2017. "Calculation of Solvency Capital Requirements for Non-life Underwriting Risk Using Generalized Linear Models," Prague Economic Papers, Prague University of Economics and Business, vol. 2017(4), pages 450-466.
    • Handle: RePEc:prg:jnlpep:v:2017:y:2017:i:4:id:621:p:450-466
    DOI: 10.18267/j.pep.621
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    References listed on IDEAS

    as
    1. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    2. Eves, Michael & Keller, Philipp, 2013. "What Solvency II firms can learn from the Swiss Solvency experience," British Actuarial Journal, Cambridge University Press, vol. 18(3), pages 503-522, September.
    3. Zaks, Yaniv & Frostig, Esther & Levikson, Benny, 2006. "Optimal Pricing of a Heterogeneous Portfolio for a Given Risk Level," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 161-185, May.
    4. Peter Liebwein, 2006. "Risk Models for Capital Adequacy: Applications in the Context of Solvency II and Beyond," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 31(3), pages 528-550, July.
    5. Tse,Yiu-Kuen, 2009. "Nonlife Actuarial Models," Cambridge Books, Cambridge University Press, number 9780521764650, December.
    6. Patrick Royston & Douglas G. Altman, 1994. "Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(3), pages 429-453, September.
    7. Gatzert, Nadine & Martin, Michael, 2012. "Quantifying credit and market risk under Solvency II: Standard approach versus internal model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 649-666.
    8. Gunther Kraut & Andreas Richter, 2015. "Insurance Regulation and Life Catastrophe Risk: Treatment of Life Catastrophe Risk Under the SCR Standard Formula of Solvency II and the Necessity of Partial Internal Models," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 40(2), pages 256-278, April.
    9. Renshaw, Arthur E., 1994. "Modelling the Claims Process in the Presence of Covariates," ASTIN Bulletin, Cambridge University Press, vol. 24(2), pages 265-285, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    claim frequency; claim severity; generalized linear models; motor insurance; non-life insurance; solvency capital requirements; Solvency II; underwriting risk;
    All these keywords.

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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