Robust maximization of asymptotic growth under covariance uncertainty

TL;DR

This paper develops a robust investment strategy for maximizing long-term growth in markets with uncertain asset covariance, using advanced mathematical tools to identify optimal strategies under model ambiguity.

Contribution

It introduces a novel approach to robust growth optimization by characterizing the optimal strategy via a generalized principal eigenvalue of a nonlinear elliptic operator, addressing covariance uncertainty.

Findings

Characterizes the optimal trading strategy under covariance ambiguity.

Links the problem to a nonlinear eigenvalue problem.

Provides a mathematical framework for robust portfolio growth maximization.

Abstract

This paper resolves a question proposed in Kardaras and Robertson [Ann. Appl. Probab. 22 (2012) 1576-1610]: how to invest in a robust growth-optimal way in a market where precise knowledge of the covariance structure of the underlying assets is unavailable. Among an appropriate class of admissible covariance structures, we characterize the optimal trading strategy in terms of a generalized version of the principal eigenvalue of a fully nonlinear elliptic operator and its associated eigenfunction, by slightly restricting the collection of nondominated probability measures.