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Thread: Geometric Brownian Motion with Markov Switching Volatility

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    Geometric Brownian Motion with Markov Switching Volatility




    Hi all,

    Suppose
    dx_{t}/x_{t}=\mu dt+\sigma_{t}dB_{t}

    where B is the standard brownian motion, and where
    \sigma_{t}\in\{\sigma_{H},\sigma_{L}\}

    with transition probability matrix between t and t+dt:
    P=\left(\begin{array}{cc}p & 1-p\\1-q & q\end{array}\right)dt

    - what is E[x_{t}|\sigma_{0}=\sigma_{H}] ?
    - what is E[x_{t}^{\alpha}|\sigma_{0}=\sigma_{H}] ?


    Any help would be highly appreciated!

    Dan

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    Re: Geometric Brownian Motion with Markov Switching Volatility


    Hi all,

    I see it's hard to get an answer on this here.
    Anyone knows a forum of stochastic calculus?

    Dan

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