The monotone follower problem in stochastic decision theory |
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Authors: | Ioannis Karatzas |
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Affiliation: | (1) Graduate School of Arts and Sciences, Department of Mathematical Statistics, Columbia University, 10027 New York, NY, USA |
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Abstract: | We consider the problem of optimally tracking the random demandx+wt, w. Brownian motion, by a nondecreasing process. adapted to the Brownian past, so as to minimize the expected lossE0T(x+wt–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. |
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