手法を比較

	破産理論	極値理論 (EVT)	確率微分方程式 (SDE)
分野	保険数理学	ファイナンス	シミュレーション
系統	Regression model	Regression model	Process / pipeline
提唱年	2010	2001	1944 (theory); 1992 (numerical framework)
提唱者	Filip Lundberg; Harald Cramér	Coles (textbook treatment); McNeil, Frey & Embrechts	Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)
種類	Stochastic risk process model	Tail / extreme-event 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	Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598	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	EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold	SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE)
関連	3	5	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.	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.	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.