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let $S(k), k\geq 0$ a discrete random process. Suppose $S(N)$ is with probability one either 100 or 0 and that $S(0)=50$. Suppose further there is at least a sixty percent probability that the price will at some point dip below 40 and then subsequently rise above 60 before time $N$. How do you prove that $S(k)$ cannot be a martingale?

By advance, thank you very much for your help.

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If this is homework, you should add the "homework" tag. –  Nate Eldredge Dec 8 '10 at 21:30

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