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https://ssrn.com/abstract=1762118
 
 

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Optimal Trend Following Trading Rules


Min Dai


National University of Singapore (NUS) - Department of Mathematics

Qing Zhang


University of Georgia - Department of Mathematics

Qiji Jim Zhu


Western Michigan University

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.

Number of Pages in PDF File: 25

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

JEL Classification: G1


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Date posted: July 20, 2011  

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

Contact Information

Min Dai (Contact Author)
National University of Singapore (NUS) - Department of Mathematics ( email )
Singapore
Qing Zhang
University of Georgia - Department of Mathematics ( email )
Department of Economics
Athens, GA 30602
United States
(706) 542-2616 (Phone)
(706) 542-2573 (Fax)
HOME PAGE: http://www.math.uga.edu/~qingz/
Qiji Jim Zhu
Western Michigan University ( email )
Kalamazoo, MI 49008
United States
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