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June, 1974 Sensitive Discount Optimality in Controlled One-Dimensional Diffusions
Martin L. Puterman
Ann. Probab. 2(3): 408-419 (June, 1974). DOI: 10.1214/aop/1176996656


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.


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Martin L. Puterman. "Sensitive Discount Optimality in Controlled One-Dimensional Diffusions." Ann. Probab. 2 (3) 408 - 419, June, 1974.


Published: June, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0286.93046
MathSciNet: MR363619
Digital Object Identifier: 10.1214/aop/1176996656

Keywords: 93 , diffusion process , E20 , expected discounted cost , piecewise constant control , Sensitive discount optimality

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 3 • June, 1974
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