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Possibilities of Individual Claim Reserve Risk Modeling

Author

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  • Pavel Zimmermann

Abstract

This article outlines possibilities of modeling the distribution of the future liabilities of an insurance company that stem from a past claim which has not yet been settled. Such a model might be used as a key component of the internal model of the reserve risk of an insurance company. It focuses on a probabilistic description of the settlement process of an individual loss, i.e., on the development of the incurred value over the lifetime of the loss. Such a model allows setting up an internal model based on an individual claim level instead of the aggregate claim level common nowadays. The proposed model respects two main restrictions given by potential industrial usage: Firstly, the model is set up in such a way that necessary data can be assumed to be available from a practical point of view. Besides that, potential requirements on the complexity of the model are considered and simplifying assumptions that allow setting up a model with 'reasonable complexity' for practical use are suggested and commented on from a practical point of view.Calibration of the model of changes in the anticipated loss (more precisely, the incurred value changes) is illustrated on real data (adjusted for confidentiality purposes). The joint modeling procedure is applied, where a generalized linear model is assumed as a model of the incurred value (response variable) as well as its response variance. Interesting properties which might be expected in similar portfolios are revealed in the data.

Suggested Citation

  • Pavel Zimmermann, 2011. "Possibilities of Individual Claim Reserve Risk Modeling," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2011(6), pages 46-64.
    • Handle: RePEc:prg:jnlaop:v:2011:y:2011:i:6:id:351:p:46-64
    DOI: 10.18267/j.aop.351
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    References listed on IDEAS

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    1. Larsen, Christian Roholte, 2007. "An Individual Claims Reserving Model," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 113-132, May.
    2. Taylor, Greg & McGuire, Gráinne & Sullivan, James, 2008. "Individual Claim Loss Reserving Conditioned by Case Estimates," Annals of Actuarial Science, Cambridge University Press, vol. 3(1-2), pages 215-256, September.
    3. 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.
    4. 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.
    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.
    6. Norberg, Ragnar, 1993. "Prediction of Outstanding Liabilities in Non-Life Insurance1," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 95-115, May.
    7. Arjas, Elja, 1989. "The Claims Reserving Problem in Non-Life Insurance: Some Structural Ideas," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 139-152, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Claims reserving; Settlement process; Generalized Linear Model; Stochastic modeling;
    All these keywords.

    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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