Robust Maximization of Asymptotic Growth Under Covariance Uncertainty
The Annals of Applied Probability (2013), Vol. 23, No. 5, pp. 1817–1840.
25 Pages Posted: 1 Feb 2014
Date Written: July 12, 2012
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.
Keywords: asymptotic growth rate, robustness, covariance uncertainty, Pucci’s operator, principal eigenvalue for fully nonlinear elliptic operators
JEL Classification: G10, G11
Suggested Citation: Suggested Citation