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| 損失分布モデル× | 確率微分方程式 (SDE)× | |
|---|---|---|
| 分野≠ | 保険数理学 | シミュレーション |
| 系統≠ | Regression model | Process / pipeline |
| 提唱年≠ | 2012 | 1944 (theory); 1992 (numerical framework) |
| 提唱者≠ | Klugman, Panjer & Willmot | Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992) |
| 種類≠ | Parametric probability model | Continuous-time stochastic process model |
| 原典≠ | 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. DOI ↗ |
| 別名≠ | Severity-Frequency Model, Aggregate Loss Model, Claim Size Distribution Model, Hasar Dağılımı Modeli | SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE) |
| 関連≠ | 3 | 4 |
| 概要≠ | 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. |
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