The monotone follower problem in stochastic decision theory

We consider the problem of optimally tracking the random demandx+w _t, w. Brownian motion, by a nondecreasing process. adapted to the Brownian past, so as to minimize the expected lossE ₀ ^T (x+w_t–_t)dt. The decision problem is reduced to a free boundary one, and the latter is studied and solved for a large class of cost functions().This research was supported in part by the Air Force Office of Scientific Research, under AF-AFOSR 77-3063.