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Shares of stock traded in a stock market. Equities represent the residual claim or interest of the most junior class of investors in assets, after all liabilities are paid.

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Probability of Closing Stock Price Over a Defined Period

Actually, the probabilities in the first case will not sum to exactly 1, since you are truncating the distribution (S' is unbounded above), but will be arbitrarily close. To get the 'right' cumulativ …
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