From Penalties to Protection: The Continuous Time Sustainable Efficiency Frontier

We develop a robust continuous time portfolio optimization framework that incorporates time-varying ESG risk through dynamically evolving drift ambiguity. Building on the equivalence between linear ESG penalties in mean-variance optimization and robust formulations under drift uncertainty, we extend the analysis to a dynamic setting with time-dependent, ESG-weighted ellipsoidal ambiguity sets. The model admits a tractable solution under CRRA preferences: the worst-case drift is obtained in closed form, and the optimal portfolio strategy is characterized as the unique maximizer of an ESG-adjusted Markowitz-type objective at each point in time. Economically, the framework provides a rigorous justification for penalty-based ESG portfolio models, while offering time-consistent robustness, forward-looking risk management, and dynamic hedging against sustainability-related model risk.