Abstract
This work develops a feasible computation procedure for trend-following trading under a bull-bear switching market model. In the asset model, the drift of the stock price switches between two parameters corresponding to an uptrend (bull market) and a downtrend (bear market) according to a partially observable Markov chain. The objective is to buy and sell the underlying stock to maximize an expected return. It is shown in Dai et al. (SIAM J Financ Math 1:780–810, 2010; Optimal trend following trading rules. Working paper) that an optimal trading strategy can be obtained in terms of two threshold levels. Finding the threshold levels turns out to be a difficult task. In this paper, we develop a stochastic approximation algorithm to approximate the threshold levels. One of the main advantages of this approach is that one need not solve the associated HJB equations. We also establish the convergence of the algorithm and provide numerical examples to illustrate the results.
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Acknowledgements
We thank Professor Qiji Zhu for fruitful discussions that led to the improvement of the computational results. This research was supported in part by the Army Research Office under W911NF-12-1-0223.
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Nguyen, D., Yin, G., Zhang, Q. (2014). A Stochastic Approximation Approach for Trend-Following Trading. In: Mamon, R., Elliott, R. (eds) Hidden Markov Models in Finance. International Series in Operations Research & Management Science, vol 209. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7442-6_7
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