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| 破产论× | 随机微分方程 (SDEs)× | |
|---|---|---|
| 领域≠ | 精算学 | 仿真 |
| 方法族≠ | Regression model | Process / pipeline |
| 起源年份≠ | 2010 | 1944 (theory); 1992 (numerical framework) |
| 提出者≠ | Filip Lundberg; Harald Cramér | Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992) |
| 类型≠ | Stochastic risk process model | Continuous-time stochastic process model |
| 开创性文献≠ | Asmussen, S., & Albrecher, H. (2010). Ruin Probabilities (2nd ed.). World Scientific. ISBN: 978-981-4282-52-9 | Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer. DOI ↗ |
| 别名≠ | Collective Risk Theory, Cramér-Lundberg Theory, Probability of Ruin Analysis, Hasar Süreci Çöküş Teorisi | SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE) |
| 相关≠ | 3 | 4 |
| 摘要≠ | 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. | 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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