In this paper we consider the problem of optimally controlling a diffusion process on a compact interval in one-dimensional Euclidean Space. Under the assumptions that the action space is finite and the cost rate, drift and diffusion coefficients are piecewise analytic, we present a constructive proof that there exist piecewise constant $n$-discount optimal controls for all finite $n \geqq 1$ and measurable $\infty$-discount optimal controls. In addition we present a sequence of second order differential equations that characterize the coefficients of the Laurent series of the expected discounted cost of an $n$-discount optimal control.
@article{1176996656,
author = {Puterman, Martin L.},
title = {Sensitive Discount Optimality in Controlled One-Dimensional Diffusions},
journal = {Ann. Probab.},
volume = {2},
number = {6},
year = {1974},
pages = { 408-419},
language = {en},
url = {http://dml.mathdoc.fr/item/1176996656}
}
Puterman, Martin L. Sensitive Discount Optimality in Controlled One-Dimensional Diffusions. Ann. Probab., Tome 2 (1974) no. 6, pp. 408-419. http://gdmltest.u-ga.fr/item/1176996656/