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Optimal stopping rules for directionally reinforced processes

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Pieter Allaart  and
Michael Monticino
Pieter Allaart*
Affiliation:
University of North Texas
Michael Monticino*
Affiliation:
University of North Texas
*
∗ Postal address: Mathematics Department, University of North Texas, Denton, TX 76203-1430, USA.
∗ Postal address: Mathematics Department, University of North Texas, Denton, TX 76203-1430, USA.
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Abstract

This paper analyzes optimal single and multiple stopping rules for a class of correlated random walks that provides an elementary model for processes exhibiting momentum or directional reinforcement behavior. Explicit descriptions of optimal stopping rules are given in several interesting special cases with and without transaction costs. Numerical examples are presented comparing optimal strategies to simpler buy and hold strategies.

Keywords

correlated random walkdirectionally reinforced random walkmultiple stoppingbuy/sell strategies

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60G50: Sums of independent random variables; random walks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 2 , June 2001 , pp. 483 - 504
Copyright
Copyright © Applied Probability Trust 2001 

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