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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  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Yu-Jui Huang

University of Colorado at Boulder - Department of Applied Mathematics

Date Written: July 12, 2012

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.

Keywords: asymptotic growth rate, robustness, covariance uncertainty, Pucci’s operator, principal eigenvalue for fully nonlinear elliptic operators

JEL Classification: G10, G11

Suggested Citation

Bayraktar, Erhan and Huang, Yu-Jui, Robust Maximization of Asymptotic Growth Under Covariance Uncertainty (July 12, 2012). The Annals of Applied Probability (2013), Vol. 23, No. 5, pp. 1817–1840.. Available at SSRN: https://ssrn.com/abstract=2388200

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Yu-Jui Huang (Contact Author)

University of Colorado at Boulder - Department of Applied Mathematics ( email )

Boulder, CO 80309
United States

HOME PAGE: http://www.yujui-huang.com

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