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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
Stochastic Modelling in Financeand Monte Carlo Simulations with R Part D: Stochastic Differential Equation Model
【摘要】 主要研究线性随机微分方程模型,为此定义It随机微积分,建立It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.
【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.
【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;
【Key words】 Monte Carlo simulations; Euler-Maruyama method; Backward Euler method; Split-Step Backward Euler method; stochastic Theta method;
【Key words】 Monte Carlo simulations; Euler-Maruyama method; Backward Euler method; Split-Step Backward Euler method; stochastic Theta method;
【基金】 国家自然科学基金(11171056,11171081)
- 【文献出处】 南京信息工程大学学报(自然科学版) ,Journal of Nanjing University of Information Science & Technology(Natural Science Edition) , 编辑部邮箱 ,2015年04期
- 【分类号】O211.63;F830
- 【被引频次】3
- 【下载频次】467