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May 2004 A homing problem for diffusion processes with control-dependent variance
Mario Lefebvre
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Ann. Appl. Probab. 14(2): 786-795 (May 2004). DOI: 10.1214/105051604000000107

Abstract

Controlled one-dimensional diffusion processes, with infinitesimal variance (instead of the infinitesimal mean) depending on the control variable, are considered in an interval located on the positive half-line. The process is controlled until it reaches either end of the interval. The aim is to minimize the expected value of a cost criterion with quadratic control costs on the way and a final cost equal to zero (resp. a large constant) if the process exits the interval through its left (resp. right) end point. Explicit expressions are obtained both for the optimal value of the control variable and the value function when the infinitesimal parameters of the processes are proportional to a power of the state variable.

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Mario Lefebvre. "A homing problem for diffusion processes with control-dependent variance." Ann. Appl. Probab. 14 (2) 786 - 795, May 2004. https://doi.org/10.1214/105051604000000107

Information

Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1061.93099
MathSciNet: MR2052902
Digital Object Identifier: 10.1214/105051604000000107

Subjects:
Primary: 93E20
Secondary: 60J60

Keywords: Brownian motion , Dynamic programming equation , hitting place , Stochastic differential equation

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.14 • No. 2 • May 2004
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