When the \bull" Meets the \bear"|a Rst Passage Time Problem for a Hidden Markov Process
نویسنده
چکیده
Let 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 diierent values when t is in diierent states. This new process Z t is a hidden Markov process. We study the probability distribution of the rst passage time for Z t. Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in nite time, there is positive probability for the bull (bear) market to become bear (bull).
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