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An Extension of Collective Risk Model for Stochastic Claim Reserving

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  • Alessandro Ricotta
  • Gian Paolo Clemente

Abstract

The evaluation of outstanding claims uncertainty plays a fundamental role in managing insurance companies. This topic has gained an increasing interest over last years because of the development of a new capital requirement framework under the Solvency II project. In particular, as results of main Quantitative Impact Studies showed, reserve risk is an essential part of underwriting risks and it has a prominent weight on the capital requirement for non-life insurance companies. To this end, we provide here a stochastic methodology in order to evaluate the distribution of claims reserve and to quantify the capital requirement for reserve risk of a single line of business. This proposal extends some existing approaches (see [12], [13], [17] and [19]) and it could represent a viable alternative to well-known methodologies in literature. Finally, a detailed numerical analysis shows a comparison between the proposed methodology and the widely used bootstrapping based on Over-Dispersed Poisson model.

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  • 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.
    • Handle: RePEc:spt:apfiba:v:6:y:2016:i:5:f:6_5_3
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    1. 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.
    2. 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.
    3. England, Peter D. & Verrall, Richard J. & Wüthrich, Mario V., 2012. "Bayesian over-dispersed Poisson model and the Bornhuetter & Ferguson claims reserving method," Annals of Actuarial Science, Cambridge University Press, vol. 6(2), pages 258-283, September.
    4. 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.
    5. 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.
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    Cited by:

    1. 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.

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