An autoregressive credibility IBNR model.

*(English)*Zbl 0837.62084Summary: An application of credibility theory to IBNR reserves is described for portfolios in which payments in consecutive development periods are determined by payments in preceding development periods, in addition to newly originating payments. For that purpose an autoregressive model is introduced and estimators for the occurring parameters are given. Furthermore, the relevance of an autoregressive structure is investigated. This is done by approximation of the mean squared prediction errors in the traditional IBNR model of T. Mack [Insure Math. Econ. 9, No. 1, 51-57 (1990; Zbl 0695.62235)] in case the risks are actually generated by an autoregressive structure. The results in this paper are applied to data on credit insurance.

##### MSC:

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

62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |

##### Keywords:

credibility theory; IBNR reserves; portfolios; autoregressive model; mean squared prediction errors; risks; credit insurance
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\textit{D. Dannenburg}, Bl., Dtsch. Ges. Versicherungsmath. 22, No. 2, 235--248 (1995; Zbl 0837.62084)

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##### References:

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[2] | Dannenburg, D. (1994a): Estimators in the Regression Credibility Model; Presented at the XXV ASTIN Colloquium in Cannes. · Zbl 0796.62091 |

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[4] | Dannenburg, D. (1995): Crossed Classification Credibility Models; Tinbergen Institute Discussion Paper, TI 95–64, Amsterdam. |

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[8] | Mack, T. (1990): Improved Estimation of IBNR Claims by Credibility Theory; Insurance: Mathematics and Economics, 9, 51–58. · Zbl 0695.62235 |

[9] | Norberg, R. (1980): Empirical Bayes Credibility; Scandinavian Actuarial Journal, 177–194. · Zbl 0447.62107 |

[10] | Norberg, R. (1986): A Contribution to Modelling of IBNR Claims; Scandinavian Actuarial Journal, 155–203. · Zbl 0648.62106 |

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