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Model uncertainty in claims reserving within Tweedie's compound Poisson models

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

    In this paper we examine the claims reserving problem using Tweedie's compound Poisson model. We develop the maximum likelihood and Bayesian Markov chain Monte Carlo simulation approaches to fit the model and then compare the estimated models under different scenarios. The key point we demonstrate relates to the comparison of reserving quantities with and without model uncertainty incorporated into the prediction. We consider both the model selection problem and the model averaging solutions for the predicted reserves. As a part of this process we also consider the sub problem of variable selection to obtain a parsimonious representation of the model being fitted.

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    File URL: http://arxiv.org/pdf/0904.1483
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0904.1483.

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    Date of creation: Apr 2009
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    Publication status: Published in ASTIN Bulletin 39(1), pp.1-33, 2009
    Handle: RePEc:arx:papers:0904.1483

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    Web page: http://arxiv.org/

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    1. Cairns, Andrew J. G., 2000. "A discussion of parameter and model uncertainty in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 27(3), pages 313-330, December.
    2. Congdon, Peter, 2006. "Bayesian model choice based on Monte Carlo estimates of posterior model probabilities," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 346-357, January.
    3. Rosenthal, Jeffrey S., 2007. "AMCMC: An R interface for adaptive MCMC," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5467-5470, August.
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    Cited by:
    1. Peters, Gareth W. & W├╝thrich, Mario V. & Shevchenko, Pavel V., 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 36-51, August.
    2. Alice X. D. Dong & Jennifer S. K. Chan & Gareth W. Peters, 2014. "Risk Margin Quantile Function Via Parametric and Non-Parametric Bayesian Quantile Regression," Papers 1402.2492, arXiv.org.

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