##
**Fitting Tweedie’s compound Poisson model to insurance claims data: dispersion modelling.**
*(English)*
Zbl 1094.91514

Summary: We reconsider the problem of producing fair and accurate tariffs based on aggregated insurance data giving numbers of claims and total costs for the claims. B. Jørgensen and M. C. P. de Souza [Scand. Actuar. J. 1994, No. 1, 69–93 (1994; Zbl 0802.62089)] assumed Poisson arrival of claims and gamma distributed costs for individual claims. Jørgensen and de Souza (loc. cit.) directly modelled the risk or expected cost of claims per insured unit, m say. They observed that the dependence of the likelihood function on m is as for a linear exponential family, so that modelling similar to that of generalized linear models is possible. In this paper we observe that, when modelling the cost of insurance claims, it is generally necessary to model the dispersion of the costs as well as their mean. In order to model the dispersion we use the framework of double generalized linear models. Modelling the dispersion increases the precision of the estimated tariffs. The use of double generalized linear models also allows us to handle the case where only the total cost of claims and not the number of claims has been recorded.

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

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

### Keywords:

car insurance; claims data; compound Poisson model; exposure; generalized linear models; dispersion modelling; double generalized linear models; power variance function; REML; risk theory; tarification### Citations:

Zbl 0802.62089
PDF
BibTeX
XML
Cite

\textit{G. K. Smyth} and \textit{B. Jørgensen}, ASTIN Bull. 32, No. 1, 143--157 (2002; Zbl 1094.91514)

Full Text:
DOI

### References:

[1] | DOI: 10.1191/147108201128140 · Zbl 1104.62080 |

[2] | DOI: 10.2307/3315676 · Zbl 0899.62088 |

[3] | Scandinavian Actuarial Journal pp 69– (1994) |

[4] | Theory of Dispersion Models (1997) |

[5] | J. R. Statist. Soc. B 49 pp 127– (1987) |

[6] | Scandinavian Actuarial Journal pp 49– (1983) |

[7] | Actuarial applications of generalized linear models. In Statistics in Finance (1998) |

[8] | An Introduction to Generalized Linear Models (2001) |

[9] | J.R. Statist. Soc B 49 pp 1– (1987) |

[10] | Data. A collection of problems from many fields for the student and research worker pp 413– (1985) |

[11] | DOI: 10.1007/BF00140865 |

[12] | J. Roy. Statist. Soc. B 51 pp 47– (1989) |

[13] | Stochastic Processes for Insurance and Finance (1999) · Zbl 0940.60005 |

[14] | DOI: 10.2143/AST.24.2.2005070 |

[15] | DOI: 10.1093/biomet/74.2.221 · Zbl 0621.62078 |

[16] | J. R. Statist. Soc. B 54 pp 273– (1992) |

[17] | Using generalized linear models to build dynamic pricing systems (2000) |

[18] | 1999 Proceedings of the Casualty Actuarial Society 86 pp 393– (1999) |

[19] | Generalized Linear Models (1989) |

[20] | Environments 10 pp 696– (1999) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.