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Optimal Trend Following Trading Rules

25 Pages Posted: 20 Jul 2011  

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Qing Zhang

University of Georgia - Department of Mathematics

Qiji Jim Zhu

Western Michigan University

Date Written: July 19, 2011

Abstract

We develop an optimal trend following trading rule in a bull-bear switching market, where the drift of the stock price switches between two parameters corresponding to an uptrend (bull market) and a downtrend (bear market) according to an unobservable Markov chain. We consider a finite horizon investment problem and aim to maximize the expected return of the terminal wealth. We start by restricting to allowing flat and long positions only and describe the trading decisions using a sequence of stopping times indicating the time of entering and exiting long positions. Assuming trading all available funds, we show that the optimal trading strategy is a trend following system characterized by the conditional probability in the uptrend crossing two threshold curves. The thresholds can be obtained by solving the associated HJB equations. In addition, we examine trading strategies with short selling in terms of an approximation. Simulations and empirical experiments are conducted and reported.

Keywords: trend following trading rule, bull-bear switching model, partial information, HJB equations

JEL Classification: G1

Suggested Citation

Dai, Min and Zhang, Qing and Zhu, Qiji Jim, Optimal Trend Following Trading Rules (July 19, 2011). Available at SSRN: https://ssrn.com/abstract=1762118 or http://dx.doi.org/10.2139/ssrn.1762118

Min Dai (Contact Author)

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Qing Zhang

University of Georgia - Department of Mathematics ( email )

Athens, GA 30602
United States
(706) 542-2616 (Phone)
(706) 542-2573 (Fax)

HOME PAGE: http://www.math.uga.edu/~qingz/

Qiji Zhu

Western Michigan University ( email )

Kalamazoo, MI 49008
United States

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