Optimal Discounted Linear Control of the Wiener Process.
Abstract
We consider the problem of discounted optimal control of the Wiener process, transformed by the action of a nonanticipative control into the state process. The latter satisfies the state equation on an appropriate probability space. There is a cost per unit time for being in the wrong state which is an even, uniformly convex function on the reals whose second derivative is decreasing with distance from the origin. There is also a cost per unit time for using the control. Both costs are discounted in time by a factor and the control action is limited. The controller has to choose a law as a nonanticipative, measurable functional of the state process with values so as to minimize the expected discounted total cost. In the present paper we proceed by formulating the control problem. The Bellman equation of dynamic programming is explicity solved and the candidate for the optimal law is discerned from the properties of the solutions. Optimality of the candidate is proved.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1979
- Accession Number
- ADA078487
Entities
People
- Ioannis Karatzas
Organizations
- Brown University