The means of the solutions are estimated through Monte Carlo method.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:We consider linearizing transformations of the one-dimensional nonlinear stochastic differential equations driven by Wiener and compound Poisson processes, namely finite activity Levy processes.
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Temel Bulgular & Veri:We apply our method to a number ofstochastic differential equations including Cox-Ingersoll-Ross short-term interest rate model, log-mean reverting asset pricing model and geometric Ornstein- Uhlenbeck equation all with additional jump terms.
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Sonuç & Katkı:The means of the solutions are estimated through Monte Carlo method.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
We consider linearizing transformations of the one-dimensional nonlinear stochastic differential equations driven by Wiener and compound Poisson processes, namely finite activity Levy processes. We present linearizability criteria and derive the required transformations. We use a stochastic integrating factor method to solve the linearized equations and provide closed-form solutions. We apply our method to a number ofstochastic differential equations including Cox-Ingersoll-Ross short-term interest rate model, log-mean reverting asset pricing model and geometric Ornstein- Uhlenbeck equation all with additional jump terms. We use their analytical solutions to illustrate the accuracy of the numerical approximations obtained from Euler and Maghsoodi discretization schemes. The means of the solutions are estimated through Monte Carlo method.
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Bu Makaleye Atıf Yap
İYİGÜNLER, İ., ÇAĞLAR, M., ÜNAL, G. (2012). Exact solvability of stochastic differential equations driven by finite activity levy processes. Mathematical and Computational Applications, Cilt: 17 - Sayı: 1, 68–82. https://ajindex.com/articles/279832
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