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Multivariate Frequency-Severity Regression Models in Insurance

Listed author(s):
  • Edward W. Frees

    ()

    (School of Business, University of Wisconsin-Madison, 975 University Avenue, Madison, WI 53706, USA)

  • Gee Lee

    ()

    (School of Business, University of Wisconsin-Madison, 975 University Avenue, Madison, WI 53706, USA)

  • Lu Yang

    ()

    (Department of Statistics, University of Wisconsin-Madison, 1300 University Avenue, Madison, WI 53706, USA)

Registered author(s):

    In insurance and related industries including healthcare, it is common to have several outcome measures that the analyst wishes to understand using explanatory variables. For example, in automobile insurance, an accident may result in payments for damage to one’s own vehicle, damage to another party’s vehicle, or personal injury. It is also common to be interested in the frequency of accidents in addition to the severity of the claim amounts. This paper synthesizes and extends the literature on multivariate frequency-severity regression modeling with a focus on insurance industry applications. Regression models for understanding the distribution of each outcome continue to be developed yet there now exists a solid body of literature for the marginal outcomes. This paper contributes to this body of literature by focusing on the use of a copula for modeling the dependence among these outcomes; a major advantage of this tool is that it preserves the body of work established for marginal models. We illustrate this approach using data from the Wisconsin Local Government Property Insurance Fund. This fund offers insurance protection for (i) property; (ii) motor vehicle; and (iii) contractors’ equipment claims. In addition to several claim types and frequency-severity components, outcomes can be further categorized by time and space, requiring complex dependency modeling. We find significant dependencies for these data; specifically, we find that dependencies among lines are stronger than the dependencies between the frequency and average severity within each line.

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    Article provided by MDPI, Open Access Journal in its journal Risks.

    Volume (Year): 4 (2016)
    Issue (Month): 1 (February)
    Pages: 1-36

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    Handle: RePEc:gam:jrisks:v:4:y:2016:i:1:p:4-:d:64467
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    1. Sun, Jiafeng & Frees, Edward W. & Rosenberg, Marjorie A., 2008. "Heavy-tailed longitudinal data modeling using copulas," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 817-830, April.
    2. Anastasios Panagiotelis & Claudia Czado & Harry Joe, 2012. "Pair Copula Constructions for Multivariate Discrete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1063-1072, September.
    3. Frees, Edward W. & Meyers, Glenn & Cummings, A. David, 2011. "Summarizing Insurance Scores Using a Gini Index," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1085-1098.
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    12. Krämer, Nicole & Brechmann, Eike C. & Silvestrini, Daniel & Czado, Claudia, 2013. "Total loss estimation using copula-based regression models," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 829-839.
    13. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, 05.
    14. Shi, Peng & Feng, Xiaoping & Ivantsova, Anastasia, 2015. "Dependent frequency–severity modeling of insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 417-428.
    15. Song, Peter X.K. & Fan, Yanqin & Kalbfleisch, John D., 2005. "Maximization by Parts in Likelihood Inference," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1145-1158, December.
    16. Patrick L. Brockett & Linda L. Golden & Montserrat Guillen & Jens Perch Nielsen & Jan Parner & Ana Maria Perez-Marin, 2008. "Survival Analysis of a Household Portfolio of Insurance Policies: How Much Time Do You Have to Stop Total Customer Defection?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 713-737.
    17. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    18. Brechmann, Eike & Czado, Claudia & Paterlini, Sandra, 2014. "Flexible dependence modeling of operational risk losses and its impact on total capital requirements," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 271-285.
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