On the approximation by the continuous time models
Project/Area Number  09630026 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Economic statistics

Research Institution  Hitotsubashi University 
Principal Investigator 
TAKAHASHI Hajime Hitotsubashi University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (70154838)

Project Fiscal Year 
1997 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,800,000 (Direct Cost : ¥2,800,000)
Fiscal Year 1999 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1998 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1997 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Keywords  Sequential Analysis / Bayes Solution / Continuous time models / Test of variance / Knock out option / 逐次分析 / ベイズ解 / 連続時間モデル / 分散の検定 / ノックアウトオプション / 分析の検定 / Sequential Test / Normal Variance / Bayes Test / Termstructure / Discret Model / Ito formulg 
Research Abstract 
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 = σ2 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).

Report
(5results)
Research Output
(10results)