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A bang-bang strategy for a finite fuel stochastic control problem

Part of: Stochastic processes Stochastic systems and control

Published online by Cambridge University Press:  01 July 2016

W. D. Sudderth  and
A. P. N. Weerasinghe
W. D. Sudderth*
Affiliation:
University of Minnesota
A. P. N. Weerasinghe*
Affiliation:
Iowa State University
*
∗Postal address: School of Statistics, University of Minnesota, 207 Vincent Hall, 206 Church Street SE, Minneapolis, MN 55455, USA.
∗∗Department of Mathematics, Iowa State University, Ames, IA 50010, USA.
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Abstract

The problem treated is that of controlling a process with values in [0, a]. The non-anticipative controls (µ(t), σ(t)) are selected from a set C(x) whenever X(t–) = x and the non-decreasing process A(t) is chosen by the controller subject to the condition where y is a constant representing the initial amount of fuel. The object is to maximize the probability that X(t) reaches a. The optimal process is determined when the function has a unique minimum on [0, a] and satisfies certain regularity conditions. The optimal process is a combination of ‘timid play' in which fuel is used gradually in the form of local time at 0, and ‘bold play' in which all the fuel is used at once.

Keywords

GAMBLINGBOLD PLAYTIMID PLAYLOCAL TIME

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 3 , September 1992 , pp. 589 - 603
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported by National Science Foundation Grants DMS-8801085 and DMS-8911548.

References

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