EMA-Type Trading Strategies Maximize Utility under Partial Information

Consider a partially informed trader who does not observe the true drift of a financial asset. Under Gaussian price dynamics with stochastic unobserved drift, including cases of mean-reversion and momentum dynamics, we take a filtering approach to solve explicitly for trading strategies which maximize expected logarithmic, exponential and power utility. We prove that the optimal strategies depend on current price and an exponentially weighted moving average (EMA) price, and in some cases current wealth, not on any other stochastic variables. We establish optimality over all price-history-dependent strategies satisfying integrability criteria, not just EMA-type strategies. Thus the condition that the optimal trading strategy reduces to a function of EMA and current price is not an assumption but rather a consequence of our analysis. We solve explicitly for the optimal parameters of the EMA-type strategies and verify optimality rigorously.