Re: A tough variance problem (at least for me)
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Sound similar to brownian motion reflection principle problems anyone?
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A simplified problem, with 0 win rate and a loss of $1000 from the original forbidden, is easily solved with the reflection method. The density at $x without ever hitting -$1000 is the unrestricted density at $x minus the unrestricted density at -$1000-(x-(-$1000)) = -$2000-x. The probability of avoiding -$1000 is probability of ending up over -$1000 minus the probability of ending up below -$1000.
The reflection method does not apply to the original problem. There is drift, and there isn't a simple forbidden region.
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