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**Analytic and bootstrap estimates of prediction errors in claims reserving.**
*(English)*
Zbl 0944.62093

Summary: We consider an appropriate residual definition for use in a bootstrap exercise to provide a computationally simple method of obtaining reserve prediction errors for a generalised linear model which reproduces the reserve estimates of the chain ladder technique (under certain restrictions which are specified in the paper). We show how the bootstrap prediction errors can be computed easily in a spreadsheet, without the need for statistical software packages. The bootstrap prediction errors are compared with their analytic equivalent from other stochastic reserving models, and also compared with other methods commonly used, including T. Mack’s distribution-free approach [ASTIN Bull. 23 No. 2, 213-225 (1993)] and methods based on log-linear models.

### MSC:

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

62G09 | Nonparametric statistical resampling methods |

62J12 | Generalized linear models (logistic models) |

### Software:

bootstrap
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\textit{P. England} and \textit{R. Verrall}, Insur. Math. Econ. 25, No. 3, 281--293 (1999; Zbl 0944.62093)

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### References:

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[6] | Mack, T., A simple parametric model for rating automobile insurance or estimating IBNR claims reserves, ASTIN bulletin, 22, 1, 93-109, (1991) |

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[12] | Renshaw, A.E., 1994. On the second moment properties and the implementation of certain GLIM based stochastic claims reserving models. Actuarial Research Paper No. 65, Department of Actuarial Science and Statistics, City University, London, EC1V 0HB. |

[13] | Renshaw, A.E., Verrall, R.J., 1994. A stochastic model underlying the chain ladder technique. Proceedings XXV ASTIN Colloquium, Cannes. |

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[15] | Verrall, R.J., On the estimation of reserves from loglinear models, Insurance: mathematics and economics, 10, 75-80, (1991) · Zbl 0723.62070 |

[16] | Verrall, R.J., Chain ladder and maximum likelihood, Journal of the institute of actuaries, 18, III, 489-499, (1991) |

[17] | Zehnwirth, B., 1989. The chain ladder technique —a stochastic model. Claims Reserving Manual, vol. 2. Institute of Actuaries, London. |

[18] | Zehnwirth, B., 1991. Interactive Claims Reserving Forecasting System (ICRFS). Insureware P/L, E. St Kilda, Victoria 3183, Australia. |

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