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Teória extrémnych hodnôt (EVT)×Model rozdelenia strát×Stochastické diferenciálne rovnice (SDR)×
OdborFinanciePoistná matematikaSimulácia
RodinaRegression modelRegression modelProcess / pipeline
Rok vzniku200120121944 (theory); 1992 (numerical framework)
TvorcaColes (textbook treatment); McNeil, Frey & EmbrechtsKlugman, Panjer & WillmotKiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)
TypTail / extreme-event modelParametric probability modelContinuous-time stochastic process model
Pôvodný zdrojColes, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598Klugman, S. A., Panjer, H. H., & Willmot, G. E. (2012). Loss Models: From Data to Decisions (4th ed.). Wiley. ISBN: 978-1-118-31532-3Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer. DOI ↗
Ďalšie názvyEVT, generalized extreme value, generalized Pareto distribution, peaks over thresholdSeverity-Frequency Model, Aggregate Loss Model, Claim Size Distribution Model, Hasar Dağılımı ModeliSDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE)
Príbuzné534
ZhrnutieExtreme 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.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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ScholarGatePorovnať metódy: Extreme Value Theory · Loss Distribution Model · Stochastic Differential Equations. Získané 2026-06-20 z https://scholargate.app/sk/compare