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An autoregressive credibility IBNR model. (English) Zbl 0837.62084
Summary: 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)
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