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Science Forum Index » Statistics - Math Forum » Optimal ratio k:1 for absorbing barriers in geometric...
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| pamela fluente... |
 Posted: Wed May 07, 2008 11:33 am |
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Guest
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I have an apparently simple question. I hope someone with some good
intuition can help me find a good direction.
Assume I buy (or sell) 1 stock, for instance GOOG or whatever.
If the price goes up (down) I will get a profit. Otherwise a loss.
Assume I close the position, selling (buying) either when:
Profit > k * 100$ (k>0, for instance k=2)
or
Loss < - 1 * 100$
So, these levels act practically providing absorbing barriers.
If I imagine the price to be modelized as a geometric brownian motion
with given volatility V
and drift randomly ranging in [-D, D] , I guess that in the very long
run (asymptotically wrt time), if I open
a lot of positions over time, the profit barrier k * 100$ should be
reached A times, while the
loss barrier -100$ should be reached B times
My simple question would be: what is a statistically reasonable (and
real world) way to infer or say something
about the value k in order to maximize the expected profit function
P(k):
P(k) = A * (k * 100$) - B * 100$
possibly based on some intelligent deduction based on the price
sequence *only* (and not just by numerous attempts, which anyway can
be useful for a verification):
Any idea or suggestion ?
-P |
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