Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 82538, 19 pages
doi:10.1155/JAMSA/2006/82538
Abstract
We consider the problem of controlling a general one-dimensional Itô diffusion by means of a finite-variation process. The objective is to minimise a long-term average expected criterion as well as a long-term pathwise criterion that penalise deviations of the underlying state process from a given nominal point as well as the expenditure of control effort. We solve the resulting singular stochastic control problems under general assumptions by
identifying an optimal strategy that is explicitly characterised.