The monotone follower problem

Author

Haussmann, Ulrich G. ; Chiarolla, Maria B.

Author_Institution

Dept. of Math. British Columbia Univ., Vancouver, BC, Canada

fYear

1992

fDate

1992

Firstpage

2053

Abstract

The monotone follower problem is a stochastic control problem in which the state, a diffusion process, is controlled by a monotone nondecreasing process. For the 1-D case it has been shown that the optimal control is singular with respect to the Lebesgue measure as a function of time and is characterized by a region of inaction A and its complement, the free boundary ∂A being reduced to a point. The present authors identify the free boundary ∂A in the 2-D case under very mild conditions. Then, they assume that A is locally of finite perimeter (LFP) and show that A can be replaced by a new region of inaction A˜. They prove that the new free boundary, ∂A˜, is countably 1-rectifiable and give conditions under which LPF holds. They show that an optimal control exists under certain conditions

Keywords

diffusion; optimal control; stochastic systems; Lebesgue measure; countably 1-rectifiable boundary; diffusion process; free boundary; inaction region; monotone follower problem; monotone nondecreasing process; singular optimal control; stochastic control problem; Costs; Diffusion processes; Discrete wavelet transforms; Equations; Indium tin oxide; Mathematics; Optimal control; Portfolios; Process control; Stochastic processes; Time measurement;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 1992., Proceedings of the 31st IEEE Conference on

Conference_Location

Tucson, AZ

Print_ISBN

0-7803-0872-7

Type

conf

DOI

10.1109/CDC.1992.371435

Filename

371435