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2005 | nr 1069 | 195
Tytuł artykułu

Teoria zaufania : modele aktuarialne

Treść / Zawartość
Warianty tytułu
Credibility Theory : Actuarial Models
Języki publikacji
PL
Abstrakty
Przedstawiono w sposób uporządkowany teorię zaufania, z uwzględnieniem najnowszych wyników oraz dokonano syntezy wyników zamieszczonych w artykułach własnych i innych autorów. Przedstawiono nowe bądź uzupełnione dowody znanych twierdzeń. Sformułowano nowe twierdzenia, tak aby przedstawiona teoria była kompletna. Teorię zilustrowano przykładami liczbowymi, wskazującymi zarówno na jej użyteczność, jak i ograniczenia.
EN
This article gives a structured overview of the development of credibility theory, which is one of the most important fields in insurance. In order to achieve this, a uniform approach and notation have been introduced and a synthesis of the results published by other authors carried out. Concepts and theorems related to linear Bayesian predictors of nett premiums are presented. A review is made regarding distribution pairs: the conditional distribution of a random variable describing a claim and the distribution of a random variable describing the structure of a non-homogeneous portfolio, whose Bayesian predictor is a predicator of credibility. Various practical models of credibility are presented, such as the Bühlmann model, together with it generalisation taking into account the importance of contracts, i.e. the Bühlmann-Straub model. Jewell's model enables us to consider a portfolio with a hierarchical structure. The case in which we observe a linear trend in the observations is considered in Hachemaister's model. Predictors of the credibility of nett premiums and estimators of parameters describing the structure of the population are derived using each of these models. In this article, for the first time statistical discrimination analysis is applied to the problem of classifying those insured in non-homogeneous portfolia. The theory presented is illustrated using simulated data. These examples show that this theory has great potential to be applied in insurance businesses. (original abstract)
Twórcy
Bibliografia
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  • ---
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  • Mayerson A. L. A Bayesian View of Credibility, "Proceedings of the Casualty Actuarial Society" 1965, 52, s. 121-127.
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  • Neuhaus W. Inference About Parameters in Empirical Linear Bayes Estimation Problems, "Scandinavian Actuarial Journal" 1984, s. 131-142.
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  • Norberg R. On optimal Parameter Estimation in Credibility, "Insurance Math. Econom." 1982, 1, s. 73-80.
  • Norberg R. Hierarchical Credibility: Analysis of a Random Effect Linear Model with Nested Classification, "Scandinavian Actuarial Journal" 1986, s. 204-222.
  • Ostasiewicz W. (red.) Modele aktuarialne, Wyd. AE, Wrocław 2000.
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  • Philbrick S. W. An Examination of Credibility Concepts, "Proceedings of the Casualty Actuarial Society" 1981, 68, s. 195-219.
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  • Sundt B. A Hierarchical Regression Credibility Model, "Scandinavian Actuarial Journal" 1979, s. 107-114.
  • Sundt B. A Multi-Level Hierarchical Credibility Regression Model, "Scandinavian Actuarial Journal" 1980, s. 25-32.
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  • Taylor G.C. Credibility Analysis of a General Hierarchical Model, "Scandinavian Actuarial Journal" 1979, s. 1-12.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
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