金融领域的随机建模与基于软件R的Monte Carlo模拟(4):随机微分方程模型

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金融领域的随机建模与基于软件R的Monte Carlo模拟(4):随机微分方程模型
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                        毛学荣毛学荣
斯特莱斯克莱德大学 数学系, 格拉斯哥, G1 1XT, 英国
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李晓月李晓月
东北师范大学 数学与统计学院, 长春, 130024
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基金项目:国家自然科学基金(11171056,11171081)

Stochastic Modelling in Financeand Monte Carlo Simulations with R Part D:Stochastic Differential Equation Model

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MAO Xuerong
MAO Xuerong
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XT, Scotland, UK
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LI Xiaoyue
LI Xiaoyue
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024
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摘要:

主要研究线性随机微分方程模型,为此定义Itô随机微积分,建立Itô公式.鉴于研究的重点是利用R软件进行数值模拟,所以详细讨论了过去10多年来随机微分方程数值解的研究.

关键词:Monte Carlo 模拟;Euler-Maruyama方法;Backward Euler方法;Split-Step Backward Euler方法;随机Theta方法

Abstract:

The key aim of this serial is to study various stochastic models in finance with emphasise on the Monte Carlo simulations with R for these models.In this paper, we will study the linear stochastic differential equation (SDE) model for the asset price.We will define the It calculus and establish the It\hat\hboxo formula.Moreover, as the Monte Carlo simulations with R is our keytopic in this serial, we will review the developments of numerical solutionsin order to highlight this very popular area in the study of SDEs.

Key words:Monte Carlo simulations;Euler-Maruyama method;Backward Euler method;Split-Step Backward Euler method;stochastic Theta method

参考文献

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[2] 毛学荣, 李晓月.金融领域的随机建模与基于软件R的Monte Carlo模拟(3):随机对数线性模型.南京信息工程大学学报:自然科学版, 2015, 7(3):214-220 MAO Xuerong, LI Xiaoyue.Stochastic modelling in finance and Monte Carlo simulations with R.Part C:Stochastic log-linear model.Journal of Nanjing University of Information Science & Technology:Natural Science Edition, 2015, 7(3):214-220

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引用本文

毛学荣,李晓月.金融领域的随机建模与基于软件R的Monte Carlo模拟(4):随机微分方程模型[J].南京信息工程大学学报(自然科学版),2015,7(4):313-322
MAO Xuerong, LI Xiaoyue. Stochastic Modelling in Financeand Monte Carlo Simulations with R Part D:Stochastic Differential Equation Model[J]. Journal of Nanjing University of Information Science & Technology, 2015,7(4):313-322

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收稿日期:2014-09-13
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在线发布日期: 2015-08-18
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