Robust Growth-Optimal Investing with Covariance Uncertainty

Summary

The paper addresses portfolio choice when an investor lacks precise knowledge of the covariance structure of the underlying assets. It seeks a strategy that maximizes asymptotic growth robustly across an appropriate class of admissible covariance structures. The work therefore focuses on how to choose investments when covariance estimates cannot be treated as known with certainty.

The authors characterize the optimal strategy using a generalized principal eigenvalue and its associated eigenfunction for a fully nonlinear elliptic operator. The characterization is established after slightly restricting the collection of probability measures that are not dominated by a common measure. The document presents a theoretical result rather than empirical performance evidence: it does not specify asset universes, numerical outcomes, or practical estimation procedures, and the result depends on the stated admissibility framework and restriction on probability measures.

Key ideas

• The problem is robust growth optimization when asset covariance is uncertain.
• The strategy is characterized over an appropriate class of admissible covariance structures.
• A generalized principal eigenvalue and its eigenfunction for a fully nonlinear elliptic operator determine the characterization.
• The result relies on a slight restriction of the considered nondominated probability measures.
• The document provides a mathematical characterization rather than reported empirical performance.

Tags

# Robust maximization of asymptotic growth under covariance uncertainty


# Robust maximization of asymptotic growth under covariance uncertainty









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.