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Another pragmatic loss reserving method or Bornhuetter-Ferguson revisited.
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Abstracts and Reviews
053056 (M31) On greatest accuracy credibility with limited fluctuation. Sundt B., Scandinavian Actuarial Journal, nr. 2, 1992, pp. 109-119. In greatest accuracy credibility theory the credibility estimator is constructed so as to be as close as possible to the estimand whereas in limited fluctuation credibility theory one tries to limit the fluctuations from year to year. It has been argued that in practice the greatest accuracy credibility estimators often give too great yearto-year fluctuations. In the present paper the authors modify the greatest accuracy credibility theory to limit these fluctuations, thus trying to combine the advantages of both theories. They also discuss other aspects of the relation between rate-making and statistical estimation (Author) theory. Keywords: Credibility, Experience Rating, Estimation, Optimality Criteria. 053057 (M31) Large claims in credibility. Kremer E., Lbhnberg, Bliitter der Deutsche Gesellschaft ftir Versicherungsmathematik, Band Xu, Heft 2, oktober 1991, pp. 123-150. The problem of how to cope with large claims in credibility rating is reconsidered. New credibility techniques are introduced leading to so called M- and Lcredibility estimators. Under certain conditions the corresponding new premium predicting formulas can be shown to be robust with respect to low-probable (extraordinary) large claims amounts. Reasonable parameter-estimation methods are presented, giving practicable (robust) empirical M- and L-credibility estimators. Also the problem of how to identify (much) larger risks in the collective is discussed and a handy detecting procedure proposed. All is done for the simplest classical credibility model and for the general regression credibility model, including the well-known (Author) Biihlmann-Straub model. Keywords: Large Claims, Credibility Theory. 053058 (M31, M42) Another pragmatic loss reserving method or Bornhuetter-Ferguson revisited. Neuhaus W., Scandinavian Actuarial Journal, nr. 2, 1992, pp. 151-162. The efficiency of an approximate credibility method for predicting outstanding claims in reinsurance, is analyzed. The advantage of the approximate method is,
that it does not require exact knowledge of the model’s second order moments. (Author) Keywords: Credibilify, Loss Reserving, Reinsurance. 053059 (M31, Mll) Stochastische Modellierung in der Erfahrungstarifierung (Stochastic modelling in experience rating). Schmidt K.D., Mannheim, Bliitter der Deutsche Gesellschaji ftir Versicherungsmathematik, Band XX, Heft 4, oktober 1992, pp. 441-445. The idea of experience rating originated early in this century and has now become one of the basic principles of both actuarial practice and insurance mathematics. Probabilistic modelling of experience rating developed slowly and was subject to several changes. The present paper focusses on some selected aspects of model building in the past and in current research: The main steps in the development up to 1970, the genesis of the classical model around 1970, and variants of the classical model with regard to effects of perturbations of certain model assumptions. (Author) Keywords: Experience Rating, Model Building. 053060 (M31, MlO) Robust credibility. Gisler A., Reinhard P., Swiss Insurance Company Winterthur, Astin Bulletin 23, nr. I, 1993, pp. I17143. Outlier observations caused by big claims or by an event producing a series of claims are a special problem in ratemaking and in tariff calculation. The authors believe that combining credibility and robust statistics is the right answer to this problem. The main idea is to robustify the individual claims experience by using a robust estimator T, instead of the individual meanX, and to look at the credibility estimator based on the robust statistics {T,: i=1,2,...}. Choosing a particular influence tinction leads to data-trimming with an observation-dependent trimming point. (Authors) Keywords: Robust Statistics, Standard Credibility Models, Data Trimming.
M40: RESERVES, GENERAL AND MISCELLANEOUS 053061 (M40) Modellberechnungen zur Reichweite der Mittel des zur bauspartechnischen Absicherung Fonds (Calculations on the range of the Technical Security
Abstracts and Reviews
053056 (M31) On greatest accuracy credibility with limited fluctuation. Sundt B., Scandinavian Actuarial Journal, nr. 2, 1992, pp. 109-119. In greatest accuracy credibility theory the credibility estimator is constructed so as to be as close as possible to the estimand whereas in limited fluctuation credibility theory one tries to limit the fluctuations from year to year. It has been argued that in practice the greatest accuracy credibility estimators often give too great yearto-year fluctuations. In the present paper the authors modify the greatest accuracy credibility theory to limit these fluctuations, thus trying to combine the advantages of both theories. They also discuss other aspects of the relation between rate-making and statistical estimation (Author) theory. Keywords: Credibility, Experience Rating, Estimation, Optimality Criteria. 053057 (M31) Large claims in credibility. Kremer E., Lbhnberg, Bliitter der Deutsche Gesellschaft ftir Versicherungsmathematik, Band Xu, Heft 2, oktober 1991, pp. 123-150. The problem of how to cope with large claims in credibility rating is reconsidered. New credibility techniques are introduced leading to so called M- and Lcredibility estimators. Under certain conditions the corresponding new premium predicting formulas can be shown to be robust with respect to low-probable (extraordinary) large claims amounts. Reasonable parameter-estimation methods are presented, giving practicable (robust) empirical M- and L-credibility estimators. Also the problem of how to identify (much) larger risks in the collective is discussed and a handy detecting procedure proposed. All is done for the simplest classical credibility model and for the general regression credibility model, including the well-known (Author) Biihlmann-Straub model. Keywords: Large Claims, Credibility Theory. 053058 (M31, M42) Another pragmatic loss reserving method or Bornhuetter-Ferguson revisited. Neuhaus W., Scandinavian Actuarial Journal, nr. 2, 1992, pp. 151-162. The efficiency of an approximate credibility method for predicting outstanding claims in reinsurance, is analyzed. The advantage of the approximate method is,
that it does not require exact knowledge of the model’s second order moments. (Author) Keywords: Credibilify, Loss Reserving, Reinsurance. 053059 (M31, Mll) Stochastische Modellierung in der Erfahrungstarifierung (Stochastic modelling in experience rating). Schmidt K.D., Mannheim, Bliitter der Deutsche Gesellschaji ftir Versicherungsmathematik, Band XX, Heft 4, oktober 1992, pp. 441-445. The idea of experience rating originated early in this century and has now become one of the basic principles of both actuarial practice and insurance mathematics. Probabilistic modelling of experience rating developed slowly and was subject to several changes. The present paper focusses on some selected aspects of model building in the past and in current research: The main steps in the development up to 1970, the genesis of the classical model around 1970, and variants of the classical model with regard to effects of perturbations of certain model assumptions. (Author) Keywords: Experience Rating, Model Building. 053060 (M31, MlO) Robust credibility. Gisler A., Reinhard P., Swiss Insurance Company Winterthur, Astin Bulletin 23, nr. I, 1993, pp. I17143. Outlier observations caused by big claims or by an event producing a series of claims are a special problem in ratemaking and in tariff calculation. The authors believe that combining credibility and robust statistics is the right answer to this problem. The main idea is to robustify the individual claims experience by using a robust estimator T, instead of the individual meanX, and to look at the credibility estimator based on the robust statistics {T,: i=1,2,...}. Choosing a particular influence tinction leads to data-trimming with an observation-dependent trimming point. (Authors) Keywords: Robust Statistics, Standard Credibility Models, Data Trimming.
M40: RESERVES, GENERAL AND MISCELLANEOUS 053061 (M40) Modellberechnungen zur Reichweite der Mittel des zur bauspartechnischen Absicherung Fonds (Calculations on the range of the Technical Security