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时滞均值回复θ过程及其数值解的收敛性
  • ISSN号：0254-7791
  • 期刊名称：《计算数学》
  • 时间：0
  • 分类：O175.1[理学—数学;理学—基础数学]
  • 作者机构：[1]东华大学应用数学系,上海200051
  • 相关基金：国家自然科学基金（11071037,60974030）资助项目
作者： 张春赛[1], 胡良剑[1]
关键词： 均值回复θ过程, 存在唯一性, 非负性, Euler-Maruyama数值解, the mean-reverting θ process, existence and uniqueness, nonnegativity, Euler-Maruyama approximate solution
中文摘要：

时滞均值回复θ过程用于描述受时间延迟影响的利率、波动率等金融特征,本文利用随机时滞微分方程理论证明了过程在1/2≤θ〈1情况时解的存在唯一性和非负性.由于表示该过程的随机时滞微分方程没有显示解,所以数值近似解是研究过程的重要的方法,本文证明了时滞均值回复θ过程Euler-Maruyama数值解的p（p≥2）阶矩意义上的强收敛性.

英文摘要：

The mean-reverting θ process with delay is used as a model for interest rates and volatility as well as other financial quantities which are past level dependent. For 1/2 ≤ θ〈 1, we prove the model has an unique nonnegative solution. Since the corresponding stochastic delay differential equation has no explicit solution, it is very important to study numerical meth- ods for the solution approximations. We prove the strong convergence of Euler-Maruyama approximate solution in sense of p-th moment（p ≥ 2）.

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期刊信息
  • 《计算数学》
  • 中国科技核心期刊
  • 主管单位:中国科学院
  • 主办单位:中国科学院数学与系统科学研究院
  • 主编：周爱辉
  • 地址：北京市海淀区中关村东路55号
  • 邮编：100190
  • 邮箱：
  • 电话：010-62555115
  • 国际标准刊号：ISSN：0254-7791
  • 国内统一刊号：ISSN：11-2125/O1
  • 邮发代号:2-521
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:4140