 
Summary: Applied Probability Trust (27 June 2003)
OPTIMAL STOPPING RULES FOR CORRELATED RANDOM
WALKS WITH A DISCOUNT
PIETER ALLAART,
University of North Texas
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
upstep, and another for stopping after a downstep. Precise expressions for
the thresholds are given both for the positively and the negatively correlated
case. The optimal rule is illustrated by several numerical examples.
Keywords: Correlated random walk; stopping rule; optimality principle;
discount factor; momentum
AMS 2000 Subject Classification: Primary 60G40; 60G50
Secondary 62L15
1. Introduction
The main goal of this paper is to answer the following basic question. Suppose an
investor owns a commodity whose price process follows a correlated random walk. If
future returns are discounted by a constant factor per unit time, when should the
