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On a constrained optimal stopping problem

Published online by Cambridge University Press:  14 July 2016

D. P. Kennedy
D. P. Kennedy*
Affiliation:
University of Cambridge
*
∗ Postal address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, U.K.
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Abstract

For a sequence of random variables {Xn , n ≧ 0}, optimal stopping is considered over stopping times T constrained so that ET ≦ α, for some fixed α > 0. It is shown that under certain circumstances a Lagrangian approach may be used to reduce the problem to an unconstrained optimal stopping problem of a conventional type. The optimal value of the natural dual problem is shown to be equal to the optimal value of the original (primal) problem when certain randomised stopping times are permitted. Two examples are considered in detail.

Keywords

OPTIMAL STOPPINGLAGRANGIANLAGRANGE MULTIPLIERSCONVEX PROGRAMMINGDUALITY

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 19 , Issue 3 , September 1982 , pp. 631 - 641
Copyright
Copyright © Applied Probability Trust 1982 

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References

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