When the "Bull" Meets the "Bear"-A First Passage Time Problem for a Hidden Markov Process

被引：13

作者：

Guo, Xin ^{[1
]}

机构：

[1] IBM TJ Watson Res Ctr, Yorktown Height, NY 10598 USA

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2001年 / 3卷 / 02期

关键词：

first passage time; the Laplace transform; hidden Markov processes; Brownian motion;

D O I：

10.1023/A:1012201109468

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let Theta(t) be a continuous Markov chain on N States. Consider adjoining a Brownian motion with this Markov chain so that the drift and the variance take different values when Theta(t) is in different states. This new process Z(t) is a hidden Markov process. We study the probability distribution of the first passage time for Z(t). Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in finite time, there is positive probability for the bull (bear) market to become bear (bull).

引用

页码：135 / 143

页数：9

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