手法を比較

	破産理論	損失分布モデル	確率微分方程式 (SDE)
分野	保険数理学	保険数理学	シミュレーション
系統	Regression model	Regression model	Process / pipeline
提唱年	2010	2012	1944 (theory); 1992 (numerical framework)
提唱者	Filip Lundberg; Harald Cramér	Klugman, Panjer & Willmot	Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)
種類	Stochastic risk process model	Parametric probability model	Continuous-time stochastic process model
原典	Asmussen, S., & Albrecher, H. (2010). Ruin Probabilities (2nd ed.). World Scientific. ISBN: 978-981-4282-52-9	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	Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer.
別名	Collective Risk Theory, Cramér-Lundberg Theory, Probability of Ruin Analysis, Hasar Süreci Çöküş Teorisi	Severity-Frequency Model, Aggregate Loss Model, Claim Size Distribution Model, Hasar Dağılımı Modeli	SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE)
関連	3	3	4
概要	Ruin Theory models the stochastic surplus process of an insurance company to quantify the probability that accumulated losses eventually exceed available capital. Introduced by Filip Lundberg in his 1903 doctoral thesis and rigorously unified by Harald Cramér in 1930, the classical Cramér-Lundberg model assumes premiums arrive at a constant rate, claims follow a compound Poisson process, and individual claim sizes are independent and identically distributed. It remains the foundational framework of collective risk theory in actuarial science.	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.	Stochastic differential equations (SDEs) are differential equation models that combine a deterministic drift term — governing the average tendency of a system — with a stochastic diffusion term driven by a Wiener process (Brownian motion). Pioneered through Itô calculus by Kiyosi Itô in 1944 and given a comprehensive numerical treatment by Kloeden and Platen in 1992, SDEs are the standard modelling language for continuous-time systems subject to random noise, including financial asset prices, population dynamics, and physical processes.