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Chain ladder method: Bayesian bootstrap versus classical bootstrap

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  • Gareth W. Peters
  • Mario V. W\"uthrich
  • Pavel V. Shevchenko
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    Abstract

    The intention of this paper is to estimate a Bayesian distribution-free chain ladder (DFCL) model using approximate Bayesian computation (ABC) methodology. We demonstrate how to estimate quantities of interest in claims reserving and compare the estimates to those obtained from classical and credibility approaches. In this context, a novel numerical procedure utilising Markov chain Monte Carlo (MCMC), ABC and a Bayesian bootstrap procedure was developed in a truly distribution-free setting. The ABC methodology arises because we work in a distribution-free setting in which we make no parametric assumptions, meaning we can not evaluate the likelihood point-wise or in this case simulate directly from the likelihood model. The use of a bootstrap procedure allows us to generate samples from the intractable likelihood without the requirement of distributional assumptions, this is crucial to the ABC framework. The developed methodology is used to obtain the empirical distribution of the DFCL model parameters and the predictive distribution of the outstanding loss liabilities conditional on the observed claims. We then estimate predictive Bayesian capital estimates, the Value at Risk (VaR) and the mean square error of prediction (MSEP). The latter is compared with the classical bootstrap and credibility methods.

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    File URL: http://arxiv.org/pdf/1004.2548
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1004.2548.

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    Date of creation: Apr 2010
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    Publication status: Published in Insurance: Mathematics and Economics (2010)
    Handle: RePEc:arx:papers:1004.2548

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    Web page: http://arxiv.org/

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    References

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    1. England, Peter & Verrall, Richard, 1999. "Analytic and bootstrap estimates of prediction errors in claims reserving," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 281-293, December.
    2. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
    3. Paulo J. R. Pinheiro & Jo´┐Żo Manuel Andrade e Silva & Maria de Lourdes Centeno, 2003. "Bootstrap Methodology in Claim Reserving," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 701-714.
    4. Pierre Del Moral & Arnaud Doucet & Ajay Jasra, 2006. "Sequential Monte Carlo samplers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 411-436.
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    Cited by:
    1. Kylie-Anne Richards & Gareth W. Peters & William Dunsmuir, 2012. "Heavy-Tailed Features and Empirical Analysis of the Limit Order Book Volume Profiles in Futures Markets," Papers 1210.7215, arXiv.org.
    2. Gareth W. Peters & Alice X. D. Dong & Robert Kohn, 2012. "A Copula Based Bayesian Approach for Paid-Incurred Claims Models for Non-Life Insurance Reserving," Papers 1210.3849, arXiv.org, revised Dec 2012.
    3. Heberle, Jochen & Thomas, Anne, 2014. "Combining chain-ladder claims reserving with fuzzy numbers," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 96-104.

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