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| Kredibilitätstheorie× | Extremwerttheorie (EVT)× | |
|---|---|---|
| Fachgebiet≠ | Versicherungsmathematik | Finanzwirtschaft |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 1967 | 2001 |
| Urheber≠ | Hans Bühlmann | Coles (textbook treatment); McNeil, Frey & Embrechts |
| Typ≠ | Weighted linear blend of individual and collective experience | Tail / extreme-event model |
| Wegweisende Quelle≠ | Bühlmann, H. (1967). Experience rating and credibility. ASTIN Bulletin, 4(3), 199–207. DOI ↗ | Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598 |
| Aliasnamen≠ | Bühlmann Credibility, Experience Rating, Linear Credibility Estimator, Güvenilirlik Teorisi | EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold |
| Verwandt≠ | 3 | 5 |
| Zusammenfassung≠ | Credibility Theory is an actuarial framework for estimating the pure premium of an individual risk by blending its own observed loss experience with the collective (portfolio) mean. Introduced by Hans Bühlmann in 1967, the method derives the optimal linear combination—the credibility-weighted premium—that minimises mean squared error. It extends classical experience rating to a rigorous statistical footing rooted in Bayesian and linear estimation principles. | Extreme Value Theory is a statistical framework for modelling the rare events that live in the tail of a probability distribution. As developed in Coles (2001) and applied to risk by McNeil, Frey & Embrechts (2005), it offers two standard routes: the Generalized Extreme Value (GEV) distribution for block maxima and the Generalized Pareto Distribution (GPD), used in the peaks-over-threshold approach, for exceedances above a high threshold. |
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