قارن الطرق

	نظرية الانهيار	المعادلات التفاضلية العشوائية (SDEs)
المجال	العلوم الاكتوارية	المحاكاة
العائلة	Regression model	Process / pipeline
سنة النشأة	2010	1944 (theory); 1992 (numerical framework)
صاحب الطريقة	Filip Lundberg; Harald Cramér	Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)
النوع	Stochastic risk process model	Continuous-time stochastic process model
المصدر التأسيسي	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.
الأسماء البديلة	Collective Risk Theory, Cramér-Lundberg Theory, Probability of Ruin Analysis, Hasar Süreci Çöküş Teorisi	SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE)
ذات صلة	3	4
الملخص	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.