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Model řetězového žebříku pro rezervace (Mackův model)×Zobecněná metoda nejmenších čtverců (GLS)×Model rozdělení ztrát×
OborPojistná matematikaStatistikaPojistná matematika
RodinaRegression modelRegression modelRegression model
Rok vzniku199319352012
TvůrceThomas MackAlexander Craig AitkenKlugman, Panjer & Willmot
TypStochastic loss reserving modelLinear estimatorParametric probability model
Původní zdrojMack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213–225. DOI ↗Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48. DOI ↗Klugman, S. A., Panjer, H. H., & Willmot, G. E. (2012). Loss Models: From Data to Decisions (4th ed.). Wiley. ISBN: 978-1-118-31532-3
Další názvyDevelopment Factor Method, Link Ratio Method, Loss Development Method, Zincir Merdiven YöntemiGLS, Aitken estimator, EGLS, feasible GLSSeverity-Frequency Model, Aggregate Loss Model, Claim Size Distribution Model, Hasar Dağılımı Modeli
Příbuzné333
ShrnutíChain-Ladder Reserving is a stochastic actuarial method for estimating outstanding claim liabilities from a run-off triangle of cumulative paid losses. Formalized by Thomas Mack in 1993, it provides distribution-free estimates of reserve amounts along with their standard errors, making it a cornerstone of property-casualty insurance reserving and regulatory practice worldwide.Generalized Least Squares (GLS) is a linear regression estimator that extends ordinary least squares to handle situations where the error terms are correlated or have non-constant variance (heteroscedasticity). Introduced by Alexander Craig Aitken in 1935, GLS achieves the Best Linear Unbiased Estimator (BLUE) under a general error covariance structure by weighting observations according to their precision, providing a theoretical bridge between OLS and modern linear mixed models.A Loss Distribution Model is a parametric statistical framework used in actuarial science to characterise the probabilistic behaviour of insurance claim amounts and frequencies. Developed comprehensively by Klugman, Panjer, and Willmot in their foundational text Loss Models: From Data to Decisions (first edition 1998, fourth edition 2012), these models underpin premium rating, reserving, reinsurance pricing, and regulatory capital calculations across the insurance and risk-management industries.
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ScholarGatePorovnat metody: Chain-Ladder Reserving · Generalized Least Squares · Loss Distribution Model. Získáno 2026-06-19 z https://scholargate.app/cs/compare