1996 Fiscal Year Final Research Report Summary
| Project/Area Number |
07630020
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Economic statistics
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| Research Institution | Hitotsubashi University |
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Principal Investigator |
TAKAHASHI Hajime Hitotsubashi Univ. Economics Professor, 経済学部, 教授 (70154838)
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| Project Period (FY) |
1995 – 1996
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| Keywords | Financial Time Series / Ito Formula / Change Point / Variance |
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| Research Abstract |
We have considered the problem of approximating the discrete time processes by the continuous time processes. The key step is to introduce the new term in the Ito formula and the some of its results are found in "On the discrete Ito formula and one factor interest rate model" (1996) Ruee Working paper #96-64 Faculty of Economics Hitotsubashi University, Kunitachi Tokyo, Japan. The results make it possible to modify the existing models on the term structure of interests rates, such as Vasicek (1977), and Heath, Jarrow and Morton (1992), discritize in more realistic fashon. We also summarized these models in the papers "On some model for the term structure of interest rates" (1966) Hitotsubashi University Research Series, Economics Vol.37,87-125, and "On some model for the term structure of interest rates II" (1966) The Annual Bulleti of the Institute for Economic Studies, Seijo University, Vol.9 103-129.
As to the problems of finding the change point of the variance of the normal random walks, we found the problem is deeply related with the Brownian motion approximation for the test process of Bays procedure which tests the normal variances. (This is pointed out to us by Prof.Chernoff). We are now considering the problem in terms of the sequential test and we are now obtaining the relevant results via the methods of backward induction.
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