手法を比較

	連鎖梯子法による準備金積立 (マックモデル)	一般化最小二乗法 (GLS)	損失分布モデル
分野	保険数理学	統計学	保険数理学
系統	Regression model	Regression model	Regression model
提唱年	1993	1935	2012
提唱者	Thomas Mack	Alexander Craig Aitken	Klugman, Panjer & Willmot
種類	Stochastic loss reserving model	Linear estimator	Parametric probability model
原典	Mack, T. (1993). Distribution-free calculation of the standard error of chain ladder reserve estimates. ASTIN Bulletin, 23(2), 213–225.	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.	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
別名	Development Factor Method, Link Ratio Method, Loss Development Method, Zincir Merdiven Yöntemi	GLS, Aitken estimator, EGLS, feasible GLS	Severity-Frequency Model, Aggregate Loss Model, Claim Size Distribution Model, Hasar Dağılımı Modeli
関連	3	3	3
概要	Chain-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.