Robust Portfolio Growth Under Model Uncertainty

Summary

The paper studies how to maximize long-run wealth growth when the market model is uncertain. It considers models constrained by a known asset region and instantaneous covariance, with an additional stability condition: the long-run occupancy measures converge to a density. The motivation for this condition is the observed stability of ranked relative market capitalizations in equity markets.

Under minimal assumptions on these inputs, the authors identify the robust growth rate with a Donsker–Varadhan rate function from occupancy-time large deviations. They also establish and explicitly characterize a trading strategy that achieves this rate across the considered models. An application treats drift uncertainty in ranked relative market capitalizations, subject to regularity assumptions after symmetrization. The excerpt describes theoretical results and a specific application, but gives no empirical performance tests or practical implementation details.

Key ideas

• The objective is to maximize investor wealth growth despite uncertainty about the market model.
• The model class fixes the asset region and instantaneous covariation while requiring stable occupancy measures.
• The robust growth rate is linked to a Donsker–Varadhan rate function.
• The authors identify a strategy that achieves the robust rate across the included models.
• The ranked capitalization application depends on regularity assumptions and is presented theoretically.

Tags

# Ergodic robust maximization of asymptotic growth


# Ergodic robust maximization of asymptotic growth









We consider the problem of robustly maximizing the growth rate of investor wealth in the presence of model uncertainty. Possible models are all those under which the assets' region $E$ and instantaneous covariation $c$ are known, and where additionally the assets are stable in that their occupancy time measures converge to a law with density $p$. This latter assumption is motivated by the observed stability of ranked relative market capitalizations for equity markets. We seek to identify the robust optimal growth rate, as well as a trading strategy which achieves this rate in all models. Under minimal assumptions upon $(E,c,p)$, we identify the robust growth rate with the Donsker-Varadhan rate function from occupancy time Large Deviations theory. We also prove existence of, and explicitly identify, the optimal trading strategy. We then apply our results in the case of drift uncertainty for ranked relative market capitalizations. Assuming regularity under symmetrization for the covariance and limiting density of the ranked capitalizations, we explicitly identify the robust optimal trading strategy in this setting.

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