Re: Bankroll Management in Limit Poker and Fractional Brownian Motion
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Fractional brownian motion is almost impossible to work with empirically. That is, you can specify a model and solve it, but it's not practical to look at real data and fit it back to a model. Tiny, high frequency variations will dominate your estimation.
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Why do you think this? People use Brownian motion to model many things and they fit specific data to the parameters of their models. Why would it be more difficult to work with FBM?
In particular, it seems clear that the "smoother" a process is, the easier it is to work with. For FBM, if the Hurst parameter is greater than 1/2, then the process is "smoother" than BM (in the sense of Holder continuity).
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A much more robust model is to assume the drift rate follows a random walk.
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Could you elaborate on the model you have in mind?
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