Optimal Trend Following Trading Rules

This paper is concerned with the optimality of a trend following trading rule. The underlying market is modeled like a bull-bear switching market in which the drift of the stock price switches between two states:the uptrend (bull market) and the down trend (bear market). We consider the case when the market mode is not directly observable and model the switching process as a hidden Markov chain. This is a continuation of our earlier study reported in Dai et al. [Dai M, Zhang Q, Zhu Q (2010) Trend following trading under a regime-switching model. SIAM J. Fin. Math. 1:780-810] where a trend following rule is obtained in terms of a sequence of stopping times. Nevertheless, a severe restriction imposed in Dai et al. [Dai M, Zhang Q, Zhu Q (2010) trend following trading under a regime-switching model. SIAM J. Fin. Math. 1:780-810] is that only a single share can be traded over time. As a result, the corresponding wealth process is not self-financing. In this paper, we relax this restriction. Our objective is to maximize the expected log-utility of the terminal wealth. We show, via a thorough theoretical analysis, that the optimal trading strategy is trend following. Numerical simulations and backtesting, in support of our theoretical findings, are also reported.