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Bayesian total loss estimation using shared random effects

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  • Baumgartner, Carolin
  • Gruber, Lutz F.
  • Czado, Claudia

Abstract

The pricing of insurance policies requires estimates of the total loss. The traditional compound model imposes an independence assumption on the number of claims and their individual sizes. Bivariate models, which model both variables jointly, eliminate this assumption. A regression approach allows policy holder characteristics and product features to be included in the model. This article presents a bivariate model that uses joint random effects across both response variables to induce dependence effects. Bayesian posterior estimation is done using Markov Chain Monte Carlo (MCMC) methods. A real data example demonstrates that our proposed model exhibits better fitting and forecasting capabilities than existing models.

Suggested Citation

  • Baumgartner, Carolin & Gruber, Lutz F. & Czado, Claudia, 2015. "Bayesian total loss estimation using shared random effects," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 194-201.
    • Handle: RePEc:eee:insuma:v:62:y:2015:i:c:p:194-201
    DOI: 10.1016/j.insmatheco.2015.02.008
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    References listed on IDEAS

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    1. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
    2. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    3. 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.
    4. J. M. Vilar & R. Cao & M. C. Ausin & C. Gonzalez-Fragueiro, 2009. "Nonparametric analysis of aggregate loss models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 149-166.
    5. Rainer Winkelmann, 2008. "Econometric Analysis of Count Data," Springer Books, Springer, edition 0, number 978-3-540-78389-3, September.
    6. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
    7. Jean-Philippe Boucher & Michel Denuit & Montserrat Guillén, 2007. "Risk Classification for Claim Counts," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 110-131.
    8. Shi, Peng & Frees, Edward W., 2011. "Dependent Loss Reserving using Copulas," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 449-486, November.
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    Cited by:

    1. Park, Sojung C. & Kim, Joseph H.T. & Ahn, Jae Youn, 2018. "Does hunger for bonuses drive the dependence between claim frequency and severity?," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 32-46.
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    3. Denuit, Michel & Lu, Yang, 2020. "Wishart-Gamma mixtures for multiperil experience ratemaking, frequency-severity experience rating and micro-loss reserving," LIDAM Discussion Papers ISBA 2020016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.
    5. Verschuren, Robert Matthijs, 2022. "Frequency-severity experience rating based on latent Markovian risk profiles," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 379-392.
    6. Chen, Zezhun & Dassios, Angelos & Tzougas, George, 2022. "EM estimation for the bivariate mixed exponential regression model," LSE Research Online Documents on Economics 115132, London School of Economics and Political Science, LSE Library.
    7. Oh, Rosy & Lee, Youngju & Zhu, Dan & Ahn, Jae Youn, 2021. "Predictive risk analysis using a collective risk model: Choosing between past frequency and aggregate severity information," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 127-139.
    8. Oh, Rosy & Jeong, Himchan & Ahn, Jae Youn & Valdez, Emiliano A., 2021. "A multi-year microlevel collective risk model," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 309-328.

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