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Math Help - Prove this :(

  1. #1
    Junior Member
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    Prove this :(

    I have an equation

    dS_{i}(t)=S_{i}(t)(\mu_{i}(t)dt+\sum^{d}_{k=1} \sigma_{ik}dW_{k}(t))

    We have a filtraiton G_t
    Show that the expectation of \frac{S_{i}(t+\triangle)-S_{i}(t)}{S_{i}(t)} |G_{t}=\mu_{i}(t)\triangle
    Last edited by Helpmeplease1; August 19th 2012 at 11:31 AM.
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  2. #2
    Junior Member
    Joined
    Nov 2011
    Posts
    31

    Re: Prove this :(

    So I'm thinking the solution of the stochastic differntial equation is

    S_{i}(t)=S_{i}(0)e^{(\mu_{i}(t)-\frac{1}{2}(\sum_{k=1}^{d}\sigma_{ik}(t))^{2})t+(\  sum_{k=1}^{d}\sigma_{ik}(t)W_{k}(t))}

    But i'm not sure what to do next
    Last edited by Helpmeplease1; August 20th 2012 at 05:29 AM.
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