Some Problems in the Optimal Control of Diffusions.
STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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We consider a class of problems in the optimal control of one-dimensional diffusion processes, with the objective to minimize expected discounted cost over an infinite planning horizon. There are available a finite number of control modes actions, and the state of the system changes locally like a Brownian Motion whose drift and variance depend upon the control mode being employed but not upon the current state. There is a holding cost which is proportional to the state of the system and is independent of the control mode. In addition to these continuous costs, there are lump costs associated with a change in action. The state space may be either a finite or semi-infinite interval, and different types of boundary behavior are considered. Absorbing barriers arise in applications to collective risk and insurance, while reflecting barriers are natural for problems in the optimal control of queueing and storage systems. When there are only two control modes, one expects an optimal policy characterized by a pair of critical numbers. For various special cases, it is shown that such an optimal policy exists, and complicated formulas for the critical numbers are derived. Author
- Statistics and Probability