期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

几何布朗运动的离散逼近及其逃逸概率的计算 被引量：1

Discrete Approximation of Geometric Brownian Motion and its Boundary Crossing Probability
下载PDF
导出
摘要 本文研究一维几何布朗运动逃逸概率的计算问题.利用Skorokhod对于随机微分方程解的离散逼近方面的研究成果,构造了一列离散马氏链,使其依分布收敛于几何布朗运动,进而利用离散马氏链的逃逸概率得到几何布朗运动逃逸概率的逼近. This work is devoted to calculate the boundary crossing probability of one-dimensional Geometric Brownian motion. Under the help of the Skorokhod approximation to the solutions of stochastic differential equations,we construct a sequence of Markov chains,which converge in distribution to Geometric Brownian motion,so that the absorption probability of these Markov chains approximates the first passage probability for the given Geometric Brownian motion.
作者 籍慧洁 史建红
机构地区 山西师范大学数学与计算机科学学院
出处 《山西师范大学学报（自然科学版）》 2016年第2期23-28,共6页 Journal of Shanxi Normal University(Natural Science Edition)
基金 山西省自然科学基金项目(2013011002-1)
关键词 逃逸概率 几何布朗运动 Skorokhod逼近 boundary crossing probability geometric brownian motion Skorokhod approximation
分类号 O213 [理学—概率论与数理统计]
  • 相关文献

参考文献6

  • 1Huijie JI,Jinghai SHAO.First passage probabilities of one-dimensional diffusion processes[J].Frontiers of Mathematics in China,2015,10(4):901-916. 被引量：2
  • 2Wang L, Potzelberger K. Crossing probabilities for diffusion processes with piecewise continuous boundaries [ J ]. Mhetodology and Computing in Applied Probability, 2007, 9:21 -40.
  • 3Potzelberger K, Wang L. Boundary crossing probability for Brownian motion[J]. J Appl Prob,2001, 38 : 152 - 164.
  • 4Novikov A, Frishling V, Kordzakhia N. Approximations of boundary crossing probabilities for a Brownian motion [ J ]. J Appl Prob, 1999,99: 1019 - 1030.
  • 5James C Fu, Tung-Lung Wu. Linear and nonlinear boundary crossing probabilities for Brownian motion and related processes [ J ]. J Appl Prob, 2010, 47 : 1058 - 1071.
  • 6Skorokhod A V. Studies in the theory of random processes [ M ]. Boston: Addison-Wesley Publishing Company, Inc, 1965.

二级参考文献18

  • 1Anderson T W. A modification of the sequential probability ratio test to reduce the sample size. Ann Math Statist, 1960, 31:165-197.
  • 2Borovkov K, Novikov A. Explicit bounds for approximation rates of boundary crossing probabilities for the Wiener process. J Appl Probab, 2005, 42:82-92.
  • 3Cai N, Chen N, Wan X. Pricing double-barrier options under a flexible jump diffusion model. Oper Res Lett, 2009, 37:163-167.
  • 4Chi Y, Lin X S. On the threshold dividend strategy for a generalized jump-diffusion risk model. Insurance Math Econom, 2011, 48(3): 326-337.
  • 5Daniels H E. Approximating the first crossing-time density for a curved boundary. Bernoulli, 1996, 2:133-143.
  • 6Downes A N, Borovkov K. First passage densities and boundary crossing probabilities for diffusion processes. Methodol Comput Appl Probab, 2008, 10:621-644.
  • 7Durbin J. The first-passage density of the Brownian motion process to a curved boundary. J Appl Probab, 1992, 29:291-304.
  • 8Ferebee B. The tangent approximation to one-sided Brownian exit densities. Z Wahrschein-lichkeitstheor Verwandte Geb, 1982, 61:309-326.
  • 9Fu J C, Wu T L. Linear and nonlinear boundary crossing probabilities for Brownian motion and related processes. J Appl Probab, 2010, 47:1058- 1071.
  • 10Giraudo M T. An approximation formula for the first-crossing-time density of a Wiener process perturbed by random jumps. Statist Probab Lett, 2009, 79:1559-1567.

共引文献1

同被引文献2

引证文献1

山西师范大学学报（自然科学版）
2016年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部