On Optimal Control of a Brownian Motion.
Abstract
This report discusses a controlled diffusion process which evolves as a reflected Brownian motion under each control action. A switching cost is incurred when the control action is switched. The control problem turns out to be a sequential decision problem, i.e., to find a sequence of optimal stopping times to switch control. The dynamic programming equation for a discounted cost criterion is a quasi-variational inequality. By allowing the discount factors tend to zero, we show a new Q.V.I. has a solution that serves as a potential function to give direction to attain the optimality for a long-run average cost criterion.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1982
- Accession Number
- ADA120370
Entities
People
- Yu-chung Liao
Organizations
- Brown University