Abstract
Let Θt 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 Θt is in different states. This new process Zt is a hidden Markov process. We study the probability distribution of the first passage time for Zt. 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).
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