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An optimal stopping problem for random walks with non-zero drift

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Markus Roters
Markus Roters*
Affiliation:
Universität Trier
*
∗Postal address: Universität Trier, FB IV Mathematik/Statistik, D-54286 Trier, Germany.
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Abstract

In this paper we give a solution of an optimal stopping problem concerning random walks with non-zero drift, thereby proving the necessity of the existence of ESτ for Wald's equation ESτ = ES1 · Ετ to hold, even if attention is restricted to non-randomized stopping times τ. This answers a question of Robbins and Samuel (1966).

Keywords

RANDOMIZED STOPPING TIMEWALD'S EQUATION

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60G50: Sums of independent random variables; random walks
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 956 - 959
Copyright
Copyright © Applied Probability Trust 1995 

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References

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