Trend-following trading using recursive stochastic optimization algorithms

This work develops with trend following trading strategies under a bull-bear market switching model. The asset model is assumed to be geometric Brownian motion type of process, in which drift of the stock price is allowed to switch between two parameters corresponding to an up-trend (bull market) and a downtrend (bear market) corresponding to a partially observable Markov chain. Our objective is to buy and sell the underlying stock to maximize an expected return. It is shown in [6], [7] that an optimal trading strategy can be obtained in terms of two threshold levels, but finding the threshold levels is a difficult task. In this paper, we develop a stochastic approximation algorithm to approximate the threshold levels. The main advantage of our method is that one need not solve the associated HamiltonJacobiBellman (HJB) equations. We establish the convergence of the algorithm and provide numerical examples to illustrate the results.