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Optimal Buy/Sell Rules for Correlated Random Walks

Part of: Stochastic processes

Published online by Cambridge University Press:  14 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, PO Box 311430, Denton, TX 76203-1430, USA.
∗Postal address: Mathematics Department, University of North Texas, PO Box 311430, Denton, TX 76203-1430, USA.
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Abstract

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Correlated random walks provide an elementary model for processes that exhibit directional reinforcement behavior. This paper develops optimal multiple stopping strategies - buy/sell rules - for correlated random walks. The work extends previous results given in Allaart and Monticino (2001) by considering random step sizes and allowing possibly negative reinforcement of the walk's current direction. The optimal strategies fall into two general classes - cases where conservative buy-and-hold type strategies are optimal and cases for which it is optimal to follow aggressive trading strategies of successively buying and selling the commodity depending on whether the price goes up or down. Simulation examples are given based on a stock index fund to illustrate the variation in return possible using the theoretically optimal stop rules compared to simpler buy-and-hold strategies.

Keywords

Correlated random walkmultiple stoppingbuy/sell strategy

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 60G50: Sums of independent random variables; random walks
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008 , pp. 33 - 44
Copyright
Copyright © Applied Probability Trust 2008 

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