Abstract
We consider the problem of optimally tracking the "random demand"x+wt, w. Brownian motion, by a nondecreasing processź. adapted to the Brownian past, so as to minimize the expected lossEź0Tź(x+wtźźt)dt. The decision problem is reduced to a free boundary one, and the latter is studied and solved for a large class of cost functionsź(ź).
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