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

Battle Count: 84

Highly relevant to quantitative trading. The paper provides a rigorous mathematical foundation for why MACD-type signals emerge as optimal estimators of latent drift information in a two-factor partial-information model. The explicit feedback controls for three standard utility functions are directly applicable to trading strategy design. The paper bridges the gap between theoretical stochastic control and practical technical analysis signals, showing that MACD is not merely an ad hoc heuristic but arises endogenously from optimal filtering and portfolio choice. The explicit formulas for optimal positions (equations 18, 21, 23) are immediately implementable.

The theoretical framework requires solving backward ODE systems (linear for log and exponential utility, Riccati for power utility) to obtain the coefficient functions Q, b, f. The Kalman-Bucy filter requires computing the time-varying drift volatility K_t and the associated covariance matrix Sigma_t. The MACD-type signal involves computing fast and slow EMA-type filters with time-varying weights alpha_t and beta_t, plus a Volterra correction operator B. The final feedback control requires evaluating m(p,f) = lambda_p * f_hat - kappa_p * P_t. Overall, the implementation is moderate: the ODE systems are standard, but the time-varying weights and Volterra correction add complexity compared to textbook MACD.

The paper is entirely theoretical with complete mathematical proofs (Theorems, Propositions, Lemmas). All derivations are self-contained and verifiable. However, there is no code, no numerical experiments, and no empirical validation. Reproducibility of the mathematical results is high given the complete proofs, but there is no computational component to reproduce.