Entropy Regularization under Bayesian Drift Uncertainty

TL;DR

This paper analyzes entropy-regularized portfolio optimization under Bayesian drift uncertainty, showing Gaussian policies are optimal, with entropy affecting policy variance and providing belief-dependent robustness.

Contribution

It derives closed-form solutions for optimal policies under Bayesian uncertainty, highlighting how entropy regularization influences policy variance and robustness.

Findings

Gaussian policies remain optimal under partial information.

Entropy regularization affects only policy variance, not mean control.

Optimal policy variance increases with posterior conviction, enhancing robustness.

Abstract

We study entropy-regularized mean-variance portfolio optimization under Bayesian drift uncertainty. Gaussian policies remain optimal under partial information, the value function is quadratic in wealth, and belief-dependent coefficients admit closed-form solutions. The mean control is identical to deterministic Bayesian Markowitz feedback; entropy regularization affects only the policy variance. Additionally, this variance does not affect information gain, and instead provides belief-dependent robustness. Notably, optimal policy variance increases with posterior conviction $|m_t|$, forcing greater action randomization when mean position is most aggressive.