金融時系列の分散構造変化問題

研究了用连续时间过程逼近离散时间过程的问题。关键的一步是在伊藤公式中引入新的术语，它的一些结果可以在“关于离散伊藤公式和单因素利率模型”（1996）Ruee工作论文#96-64中找到，一桥大学经济系，Kunitachi东京，日本。这些结果使得修改现有的利率期限结构模型成为可能，如Vasicek（1977）和Heath， Jarrow和Morton（1992）以更现实的方式进行区分。我们还在论文“关于利率期限结构的某些模型”（1966）一桥大学研究系列，经济学第37卷，87-125，和“关于利率期限结构的某些模型II”（1966）经济研究所年度公报，Seijo大学，第9卷，103-129中总结了这些模型。对于寻找正态随机游走方差变化点的问题，我们发现这个问题与检验正态方差的bayes方法的检验过程中的布朗运动近似密切相关。（这是切尔诺夫教授向我们指出的）。我们现在用顺序检验的方法来考虑这个问题，我们现在通过逆向归纳法得到相关的结果。

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.