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Bayesian Estimation of Structure Variables in the Collective Risk Model for Reserve Risk

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  • Alessandro Ricotta
  • Edoardo Luini

Abstract

Reserve risk represents a fundamental component of underwriting risk for non-life insurers and its evaluation can be achieved through a wide range of stochastic approaches, including the Collective Risk Model. This paper, in order to fill a gap in existing literature, proposes a Bayesian technique aimed at evaluating the standard deviation of structure variables embedded into the Collective Risk Model. We adopt uninformative prior distributions and the observations of the statistical model are obtained making use of Mack’s formula linked to bootstrap methodology. Moreover, correlation between structure variables is investigated with a Bayesian method, where a dependent bootstrap approach is adopted. Finally, a case study is carried out: the Collective Risk Model is used to evaluate the claims reserve of two non-life insurers characterized by a different reserve size. The claims reserve distribution is examined with respect to the total run-off and the one-year time horizon, enabling the assessment of the reserve risk capital requirement. JEL classification numbers: G22, C63Keywords: stochastic claims reserving, collective risk model, structure variables, Bayesian approach, bootstrap.

Suggested Citation

  • Alessandro Ricotta & Edoardo Luini, 2019. "Bayesian Estimation of Structure Variables in the Collective Risk Model for Reserve Risk," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 9(2), pages 1-2.
    • Handle: RePEc:spt:apfiba:v:9:y:2019:i:2:f:9_2_2
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    References listed on IDEAS

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    1. Peters, Gareth W. & Wüthrich, 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. England, P. D. & Verrall, R. J., 2006. "Predictive Distributions of Outstanding Liabilities in General Insurance," Annals of Actuarial Science, Cambridge University Press, vol. 1(2), pages 221-270, September.
    3. Mack, Thomas, 1993. "Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 213-225, November.
    4. Mario V. Wuthrich & Michael Merz, 2015. "Stochastic Claims Reserving Manual: Advances in Dynamic Modeling," Swiss Finance Institute Research Paper Series 15-34, Swiss Finance Institute.
    5. Alessandro Ricotta & Gian Paolo Clemente, 2016. "An Extension of Collective Risk Model for Stochastic Claim Reserving," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 6(5), pages 1-3.
    6. Mack, Thomas, 1999. "The Standard Error of Chain Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 361-366, November.
    7. Ohlsson, Esbjörn & Lauzeningks, Jan, 2009. "The one-year non-life insurance risk," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 203-208, October.
    8. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(3), pages 443-518, August.
    9. David Scollnik, 2001. "Actuarial Modeling with MCMC and BUGs," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 96-124.
    10. Gareth W. Peters & Mario V. Wuthrich & Pavel V. Shevchenko, 2010. "Chain ladder method: Bayesian bootstrap versus classical bootstrap," Papers 1004.2548, arXiv.org.
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    More about this item

    Keywords

    stochastic claims reserving; collective risk model; structure variables; bayesian approach; bootstrap.;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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