Portfolio Optimization under Fast and Slow Latent Mean-Reverting and Momentum Drift

Abstract

We consider a class of partial-information portfolio optimization problems in which the drift of a risky asset is driven by two latent stochastic factors evolving at distinct time scales. We show that the filtered estimate of the latent mean-reversion level is driven by the difference between fast and slow exponential moving average (EMA)-type processes of the trailing price history, yielding a Moving Average Convergence Divergence (MACD)-type signal, along with a deterministic Volterra correction. Under logarithmic, power, and exponential utility, we derive candidate optimal strategies in explicit feedback form and establish admissibility and verification results. In particular, the results provide a mathematical foundation for the endogenous emergence of MACD-type trading signals as estimators of latent drift information contained in observed price paths.