Path Space Robust Bayesian Portfolio Selection

The paper studies a Bayesian investor who estimates an unknown asset drift via Kalman-Bucy filtering and trades a mean-variance optimal portfolio, but who worries his model of observed prices is wrong. It builds a robust version of the strategy that guards against an adversary distorting the price dynamics (penalized by relative entropy), and derives closed-form results for the robust policy and the cost of that robustness. Key findings: robustness costs roughly half the variance of the loss a non-robust investor would face, and the robust policy shrinks large positions via a cubic correction.

Why it matters: It formalizes how to make a learning-based mean-variance strategy less fragile to model misspecification, showing robustness naturally pulls back oversized bets. The closed-form 'price of robustness' could help practitioners think about how much expected performance to sacrifice for protection against a wrong observation model.

• Robustness leads to shrinking large positions through a cubic correction, curbing over-leveraged bets.
• The leading-order cost of robustness equals about half the variance of the non-robust investor's loss.
• With a known drift the non-robust policy is infinitely costly, but under learning the loss and cost stay bounded.
• The affine policy structure is preserved when the robustness penalty is scaled by value.

⚠ This is a theoretical continuous-time model with closed-form results under specific assumptions (Brownian dynamics, entropy penalty); it is not tested on real data or live trading.