金融時系列の分散構造変化問題

我们考虑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项，它的一些结果见于1996年鲁伊工作论文#96-东京一桥大学经济学院的《关于离散的伊藤公式和单因素利率模型》。这些结果使得修正现有的利率期限结构模型成为可能，如Vasicek(1977)和Heath，Jrow and Morton(1992)，用更现实的Fashon描述。在《利率期限结构的某些模型》(1966)和《利率期限结构的某些模型》(1966)一桥大学研究系列，第37卷，第87-125卷，以及《利率期限结构的某些模型II》(1966)的论文《关于利率期限结构的一些模型》(第9卷103-129期)中，我们也对这些模型进行了总结。(这是切尔诺夫教授向我们指出的)。我们现在正在从序贯检验的角度来考虑这个问题，并正在通过向后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.