When the “Bull” Meets the “Bear”—A First Passage Time Problem for a Hidden Markov Process

Xin Guo ()
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Xin Guo: IBM T. J. Watson Research Center

Methodology and Computing in Applied Probability, 2001, vol. 3, issue 2, 135-143

Abstract: 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).

Keywords: first passage time; the Laplace transform; hidden Markov processes; Brownian motion (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1012201109468

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