On the approximation by the continuous time models

关于连续时间模型的近似

基本信息

批准号：
09630026
负责人：
TAKAHASHI Hajime
金额：
$ 1.79万
依托单位：
Hitotsubashi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09630026/
关键词：
Sequential Analysis Bayes Solution Continuous time models Test of variance Knock out option 分析の検定 Sequential Test Normal Variance Bayes Test Termstructure Discret Model Ito formulg

项目摘要

The object of this project is to carry out an experiment on the ability to apply the optimal sequential test for determining the sign of a normal mean as an approximation to the solution of a large class of sequential testing problems. Two potential advantages of such an approximation, if it is proved to be effective, are that it is easy to calculate and that it can be expressed simply in terms of a single easily interpreted curve, determine the optimal stopping time. Incidentally one version of that curve is one where a normal significance level for stopping is expressed as a function of the information obtained to date.The experiment consists of comparing the approximation to the optimal Bayes solution for the sequential test that the standard deviation of a normal distribution exceeds one. In this problem the unknown value of θ = σ-2 is assumed to have a gamma distribution. The naive application of the central limit theorem gives us unsatisfactory approximations. The Edgeworth type approximation has been considered together with the continuous time approximation for the discrete time processes. The numerically satisfactory results have not been obtained yet. The constant proposed by Hogan (1986, Ann. Statists.) is obtained for the gamma random walk.Another problem considered in this project is the pricing of the exponentially square root curved boundary knockout type European type option. We have obtained the pricing formula, a part of which has been published (Morimoto, M 1999, Ph.D. thesis Boston University).

该项目的目的是对应用最佳顺序测试的能力进行实验，以确定正常均值的符号，作为与大型顺序测试问题解决方案的近似值。这种近似值的两个潜在优势，如果被证明是有效的话，它很容易计算，并且可以简单地以单个易于解释的曲线表示，请确定最佳的停止时间。顺便说一句，该曲线的一个版本是一个版本，其中停止的正常显着性水平是作为迄今为止获得的信息表示的。在此问题中，假定θ=σ-2的未知值具有γ分布。中央限制定理的幼稚应用使我们近似不令人满意。 Edgeworth类型的近似与离散时间过程的连续时间近似一起考虑。尚未获得数值令人满意的结果。 Hogan（1986，Ann。statists。）提出的常数是为伽马随机步行而获得的。该项目中考虑的另一个问题是定价正方形的平方根弯曲边界敲除欧洲类型的选项。我们已经获得了定价公式，其中一部分已出版（Morimoto，M 1999，博士学位论文波士顿大学）。