Probabilistic aspects of finite-fuel stochastic control.
The problem is that of following the Brownian path by a nondecreasing, bounded process in such a way as to minimize the expected cost over a finite horizon. Using purely probabilistic arguments, one obtains a fairly explicit representation for the value of this problem, as well as information about the nature of the optimal process.
Karatzas
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Department of Statistics, Columbia University, New York, NY 10027.