Prognoses for a Non-Predictable Discounted Commodity Price Process
We consider the behavior of the price of a continuously stored commodity, for which discounted price is a non-constant martingale, and thus not-predictable. We prove that the discounted price realization is within any given neighborhood of zero, with any given probability less than 1, beyond a finite state-independent horizon. Furthermore, with probability 1, the path of discounted price realizations will lie permanently within any given neighborhood of zero beyond a finite state-dependent horizon. The martingale property implies that for a sufficiently long series of initial dates, the average of returns over a given horizon approximates the opportunity cost of capital arbitrarily exactly. But the average of returns for the same initial dates, over a sufficiently extended horizon, reflects the eventual and permanent downward divergence of price realizations from any profile of conditional expectations.
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