Payandeh Najafabadi, Amir T.
(2010):
*A new approach to the credibility formula.*
Published in: Insurance: Mathematics and Economics
No. 46
(2010): pp. 334-338.

Preview |
PDF
MPRA_paper_21587.pdf Download (455kB) | Preview |

## Abstract

The usual credibility formula holds whenever, (i) claim size distribution is a member of the exponential family of distributions, (ii) prior distribution conjugates with claim size distribution, and (iii) square error loss has been considered. As long as, one of these conditions is violent, the usual credibility formula no longer holds. This article, using the mean square error minimization technique, develops a simple and practical approach to the credibility theory. Namely, we approximate the Bayes estimator with respect to a general loss function and general prior distribution by a convex combination of the observation mean and mean of prior, say, approximate credibility formula. Adjustment of the approximate credibility for several situations and its form for several important losses are given.

Item Type: | MPRA Paper |
---|---|

Original Title: | A new approach to the credibility formula |

English Title: | A new approach to the credibility formula |

Language: | English |

Keywords: | Loss function Balanced loss function Mean square error technique |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General |

Item ID: | 21587 |

Depositing User: | Amir/T Payandeh |

Date Deposited: | 13 Apr 2010 02:29 |

Last Modified: | 26 Sep 2019 10:31 |

References: | Atanasiu, V., 2008. Contributions to the credibility theory. Applied Sciences 10, 1928. Bailey, A., 1950. A generalized theory of credibility. Proceedings of the Casualty Actuarial Society 13, 1320. Bouchera, J.P., Denuit, M., 2008. Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation. Insurance: Mathematics and Economics 42 (2), 727735. Bühlmann, H., 1967. Experience rating and credibility. Astin Bulletin 4 (3), 199207. Bühlmann, H., Gisler, A., 2005. A Course in Credibility Theory and its Applications. Springer, Netherlands. Bülmann, H., Straub, E., 1970. Glaubwüdigkeit für Schadensze. Bulletin of the Swiss Association of Actuaries 70, 111133. Diaconis, P., Ylvisaker, D., 1979. Conjugate priors for exponential families. The Annals of Statistics 7, 269281. Gisler, A., Wüthrich, M.V., 2008. Credibility for the chain ladder reserving method. Astin Bulletin 38 (2), 565600. Gómez-Déniz, E., 2006. On the use of the weighted balanced loss function to obtain credibility premiums. In: Proceeding of the International Conference on Mathematical and Statistical Modeling in Honor of Enrique Castillo, pp. 112. Gómez-Déniz, E., 2007. A generalization of the credibility theory obtained by using the weighted balanced loss function. Insurance: Mathematics and Economics 42, 850854. Goovaerts, M.J., Hoogstad, W.J., 1987. Credibility Theory. In: Surveys of Actuarial Studies, vol. 4. Nationale-Nederlanden N.V., Rotterdam. Herzog, T.N., 1996. Introduction to Credibility Theory, 2nd ed. ACTEX Publications, Winsted. Jafari Jozani, M., Marchand, E., Parsian, A., 2006. Bayes estimation under a general class of balanced loss functions. Technical report No. 36, Université de Sherbrooke. Kaas, R., Dannenburg, D., Goovaerts, M., 1996. Exact credibility for weighted observations. Astin Bulletin 27 (2), 287295. Klugman, S.A., Panjer, H.H., Willmot, G.E., 2004. Loss Models: From Data to Decisions. John Wiley & Sons, New York. Landsman, Z., 2002. Credibility theory: A new view from the theory of second order optimal statistics. Insurance: Mathematics and Economics 30, 351362. Lehmann, E.L., Romano, J.P., 2005. Testing Statistical Hypotheses. Springer-Verlag, New York. Marchand, E., Payandeh, A., 2009. On the behavior of Bayes' estimators, under symmetric and strictly bowl-shaped loss function, preprint. Mowbray, A., 1914. How extensive a payroll is necessary to give dependable pure premium? Proceedings of the Casualty Actuarial Society 1, 2430. Norberg, R., 2004. Credibility theory. In: Encyclopedia of Actuarial. John Wiley & Sons, pp. 398406. Rejesus, R.M., Coble, K.H., Knight, T.O., Jin, Y., 2006. Developing experience-based premium rate discounts in crop insurance. American Journal of Agricultural Economics 88, 409419. Whitney, A., 1918. The theory of experience rating. Proceedings of the Casualty Actuarial Society 4, 274292. Zellner, A., 1994. Bayesian and non-Bayesian estimation using balanced loss function. In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics. Springer, New York, pp. 371390. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/21587 |