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Estimation of loss reserves with lognormal development factors

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  • Han, Zhongxian
  • Gau, Wu-Chyuan

Abstract

This paper uses a development technique to estimate the loss reserve in a classical run-off triangle setting. Closed-form solutions for unbiased estimates of reserves and their corresponding standard errors can be obtained by assuming lognormal distributions of the development factors. The technique is applied to the Bornhuetter-Ferguson method [Bornhuetter, R.L., Ferguson, R.E., 1972. The actuary and IBNR. Proc. Casualty Actuarial Soc. 59, 181-195] and to two previously studied data sets.

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  • Han, Zhongxian & Gau, Wu-Chyuan, 2008. "Estimation of loss reserves with lognormal development factors," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 389-395, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:389-395
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    References listed on IDEAS

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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. 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. Enrique de Alba, 2002. "Bayesian Estimation of Outstanding Claim Reserves," North American Actuarial Journal, Taylor & Francis Journals, vol. 6(4), pages 1-20.
    4. Verrall, R. J., 1991. "On the estimation of reserves from loglinear models," Insurance: Mathematics and Economics, Elsevier, vol. 10(1), pages 75-80, March.
    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. Taylor, G. C. & Ashe, F. R., 1983. "Second moments of estimates of outstanding claims," Journal of Econometrics, Elsevier, vol. 23(1), pages 37-61, September.
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    Cited by:

    1. Boratyńska, Agata, 2017. "Robust Bayesian estimation and prediction of reserves in exponential model with quadratic variance function," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 135-140.
    2. Guillen, Montserrat & Prieto, Faustino & Sarabia, José María, 2011. "Modelling losses and locating the tail with the Pareto Positive Stable distribution," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 454-461.
    3. Michelle S. Goeree & John C. Ham & Daniela Iorio, 2009. "Caught in the bulimic trap? Persistence and state dependence of bulimia among young women," IEW - Working Papers 447, Institute for Empirical Research in Economics - University of Zurich, revised Jul 2012.

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