A comparative study of numerical simulation of stochastic differential equations. Application to stochastic Duffing-oscillator

Riadh, Baazaoui; Ouerdiane, Habib

doi:10.12988/ijma.2014.27188

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…Milstein's method or Runge-Kutta method e.g. [5]. These three methods improve the approximation of the solution by applying higher order extension of the SDE solution in the Ito -Taylor series e.g.…”

Section: Numerical Methods To Solve the Stochastic Differential Equatmentioning

confidence: 99%

Numerical methods for solution of the stochastic differential equations equivalent to the non-stationary Parkers transport equation

Wawrzyńczak

Modzelewska

Kluczek

2015

J. Phys.: Conf. Ser.

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We derive the numerical schemes for the strong order integration of the set of the stochastic differential equations (SDEs) corresponding to the non-stationary Parker transport equation (PTE). PTE is 5-dimensional (3 spatial coordinates, particles energy and time) Fokker-Planck type equation describing the non-stationary the galactic cosmic ray (GCR) particles transport in the heliosphere. We present the formulas for the numerical solution of the obtained set of SDEs driven by a Wiener process in the case of the full three-dimensional diffusion tensor. We introduce the solution applying the strong order Euler-Maruyama, Milstein and stochastic Runge-Kutta methods. We discuss the advantages and disadvantages of the presented numerical methods in the context of increasing the accuracy of the solution of the PTE.

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Section: Numerical Methods To Solve the Stochastic Differential Equatmentioning

confidence: 99%

Numerical methods for solution of the stochastic differential equations equivalent to the non-stationary Parkers transport equation

Wawrzyńczak

Modzelewska

Kluczek

2015

J. Phys.: Conf. Ser.

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“…Na literatura especializada, vários métodos numéricos específicos para a integração de modelos estocásticos podem ser encontrados (Schaffter, 2009, Riadh, 2014. Nesta seção, são destacadas algumas metodologias para a integração de EDEs de primeira ordem representadas pelo processo de Itô (Oksendal, 1952): A seguir são apresentados os principais métodos numéricos propostos para resolver equações diferenciais estocásticas de primeira ordem.…”

Section: Métodos Numéricos Estocásticosunclassified

Simulação do Processo de Cristalização usando Métodos Numéricos Estocásticos

Lobato

Santos²

2020

Cereus

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Simulação do Processo de Cristalização usando Métodos Numéricos Estocásticos Simulation of Crystallization Process using Stochastic Numerical Methods RESUMOTradicionalmente, durante a simulação de sistemas de Engenharia e áreas afins, não se considera a presença de incertezas nas variáveis, nos parâmetros ou nos modelos que caracterizam o fenômeno em análise. Nesse contexto, deixa-se de avaliar a influência dessas incertezas nos perfis obtidos. Desde o ano de 1965, o interesse pela resolução de modelos estocásticos tem atraído a atenção da comunidade científica, visto que todo modelo fenomenológico apresenta, no mínimo, incerteza associada às hipóteses consideradas durante sua formulação. Diante do que foi apresentado, este trabalho tem como objetivo simular um processo de cristalização em que são consideradas incertezas na concentração de cristais. Para essa finalidade, consideram-se vários métodos numéricos estocásticos para a resolução do modelo matemático (balanço de massa e balanço populacional) que representa este processo. Inicialmente, estes métodos são aplicados a dois problemas matemáticos clássicos que apresentam solução analítica. A partir dos resultados obtidos, observase a qualidade da solução em função da qualidade do método numérico estocástico considerado.

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Stochastic Ito-Calculus and Numerical Approximations for Asset Price Forecasting in the Nigerian Stock Market

Urama¹,

Ezepue²

2018

JMF

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Predicting prices of financial assets have always been topical in finance. This conceptual paper considers the seminal paper by Black-Scholes [1], how to determine the parameters of the geometric Brownian motion, and their use in forecasting stock prices, especially for cases where analytic solutions are not feasible. Generally describing stock market dynamics and heuristic modelling of derivative prices in the Nigerian Stock Market (NSM), the paper particularly uses data on the stock prices of a Nigerian bank to develop the stochastic calculus foundations of such modelling. The bank stock prices are part of daily closing stock prices of 82 stocks listed and fully traded in the NSM between 3 August 2009 and 26 August 2013, which support wider heuristic modelling foreshadowed by the paper. Technically, the paper considers the use of accurate numerical approximation method to simulate nonlinear solutions to stochastic differential Equations (SDE) resulting from asset prices. Importantly, the paper illustrates the workings of the standard Black-Scholes results as a preparation for more detailed empirical modelling of some candidate derivative pricing formulae in the Nigerian Stock Market (NSM). It particularly illustrates the dual use of the BS [1] model and the Euler-Maruyama (EM) model for pricing, respectively, the derivative and underlying assets in a financial market, for example the NSM. The paper will help the Nigerian Stock Exchange to use derivatives to deepen the NSM. The specific objectives of the paper and the notes on policy implications provide the rudiments of theory and follow-on heuristics for this goal. Also, academics and practitioners can use the results as starting points for enhancing the research and

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A comparative study of numerical simulation of stochastic differential equations. Application to stochastic Duffing-oscillator

Cited by 3 publications

References 6 publications

Numerical methods for solution of the stochastic differential equations equivalent to the non-stationary Parkers transport equation

Numerical methods for solution of the stochastic differential equations equivalent to the non-stationary Parkers transport equation

Simulação do Processo de Cristalização usando Métodos Numéricos Estocásticos

Stochastic Ito-Calculus and Numerical Approximations for Asset Price Forecasting in the Nigerian Stock Market

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