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Bayesian modelling of the time delay between diagnosis and settlement for Critical Illness Insurance using a Burr generalised-linear-type model

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  • Ozkok, Erengul
  • Streftaris, George
  • Waters, Howard R.
  • Wilkie, A. David
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    Abstract

    We discuss Bayesian modelling of the delay between dates of diagnosis and settlement of claims in Critical Illness Insurance using a Burr distribution. The data are supplied by the UK Continuous Mortality Investigation and relate to claims settled in the years 1999–2005. There are non-recorded dates of diagnosis and settlement and these are included in the analysis as missing values using their posterior predictive distribution and MCMC methodology. The possible factors affecting the delay (age, sex, smoker status, policy type, benefit amount, etc.) are investigated under a Bayesian approach. A 3-parameter Burr generalised-linear-type model is fitted, where the covariates are linked to the mean of the distribution. Variable selection using Bayesian methodology to obtain the best model with different prior distribution setups for the parameters is also applied. In particular, Gibbs variable selection methods are considered, and results are confirmed using exact marginal likelihood findings and related Laplace approximations. For comparison purposes, a lognormal model is also considered.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167668711001326
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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 50 (2012)
    Issue (Month): 2 ()
    Pages: 266-279

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    Handle: RePEc:eee:insuma:v:50:y:2012:i:2:p:266-279

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: Bayesian analysis; Burr distribution; Critical illness insurance; Diagnosis–settlement time lag; Generalised-linear-type models; Gibbs variable selection; MCMC;

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    1. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    2. Katrien Antonio & Jan Beirlant, 2008. "Issues in Claims Reserving and Credibility: A Semiparametric Approach With Mixed Models," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 643-676.
    3. Beirlant, Jan & Goegebeur, Yuri & Verlaak, Robert & Vynckier, Petra, 1998. "Burr regression and portfolio segmentation," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 231-250, December.
    4. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    5. Ioannis Ntzoufras, . "Gibbs Variable Selection using BUGS," Journal of Statistical Software, American Statistical Association, vol. 7(i07).
    6. Beirlant, Jan & Goegebeur, Yuri, 2003. "Regression with response distributions of Pareto-type," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 595-619, April.
    7. Christophe Dutang & Vincent Goulet & Mathieu Pigeon, . "actuar: An R Package for Actuarial Science," Journal of Statistical Software, American Statistical Association, vol. 25(i07).
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