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| 極値理論 (EVT)× | 破産理論× | |
|---|---|---|
| 分野≠ | ファイナンス | 保険数理学 |
| 系統 | Regression model | Regression model |
| 提唱年≠ | 2001 | 2010 |
| 提唱者≠ | Coles (textbook treatment); McNeil, Frey & Embrechts | Filip Lundberg; Harald Cramér |
| 種類≠ | Tail / extreme-event model | Stochastic risk process model |
| 原典≠ | Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598 | Asmussen, S., & Albrecher, H. (2010). Ruin Probabilities (2nd ed.). World Scientific. ISBN: 978-981-4282-52-9 |
| 別名≠ | EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold | Collective Risk Theory, Cramér-Lundberg Theory, Probability of Ruin Analysis, Hasar Süreci Çöküş Teorisi |
| 関連≠ | 5 | 3 |
| 概要≠ | 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. | 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. |
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