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Optimal stopping rules for correlated random walks with a discount

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  14 July 2016

Pieter Allaart
Pieter Allaart*
Affiliation:
University of North Texas
*
∗ Postal address: Mathematics Department, University of North Texas, PO Box 311430, Denton, TX 76203-1430, USA. Email address: allaart@unt.edu
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Abstract

Optimal stopping rules are developed for the correlated random walk when future returns are discounted by a constant factor per unit time. The optimal rule is shown to be of dual threshold form: one threshold for stopping after an up-step, and another for stopping after a down-step. Precise expressions for the thresholds are given for both the positively and the negatively correlated cases. The optimal rule is illustrated by several numerical examples.

Keywords

Correlated random walkstopping ruleoptimality principlediscount factormomentum

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60G50: Sums of independent random variables; random walks
Secondary: 62L15: Optimal stopping
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 483 - 496
Copyright
Copyright © Applied Probability Trust 2004 

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