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1999 Fiscal Year Final Research Report Summary

On the approximation by the continuous time models

Research Project

Project/Area Number 09630026
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Economic statistics
Research InstitutionHitotsubashi 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 Period (FY) 1997 – 1999
KeywordsSequential Analysis / Bayes Solution / Continuous time models / Test of variance / Knock out option
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 = 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).

  • Research Products

    (5 results)

All Other

All Publications (5 results)

  • [Publications] H. Takahashi: "A note on interaction between markets"Asia-Pacific Financial Markets. 7. (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Takahashi: "On the discrete time and continuous states models"Hitotsubashi Journal of Economics. 38. 125-137 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 高橋一: "経済とファイナンスのための数学"新世社. 223 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Hajime Takahashi: "A Note on interaction between financial markets"Asia-Pacific Financial Markets. Vol. 7, No. 4. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hajime Takahashi: "On the descrete and continuous time models"Hitotsubashi Journal of Economics. Vol. 38. 125-139 (1997)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2001-10-23  

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