The Annals of Applied Probability

Robust maximization of asymptotic growth under covariance uncertainty

Erhan Bayraktar and Yu-Jui Huang

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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.

Article information

Source
Ann. Appl. Probab., Volume 23, Number 5 (2013), 1817-1840.

Dates
First available in Project Euclid: 28 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1377696299

Digital Object Identifier
doi:10.1214/12-AAP887

Mathematical Reviews number (MathSciNet)
MR3114918

Zentralblatt MATH identifier
1287.60081

Subjects
Primary: 60G44: Martingales with continuous parameter 60H05: Stochastic integrals 47J10: Nonlinear spectral theory, nonlinear eigenvalue problems [See also 49R05] 49K35: Minimax problems

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

Citation

Bayraktar, Erhan; Huang, Yu-Jui. Robust maximization of asymptotic growth under covariance uncertainty. Ann. Appl. Probab. 23 (2013), no. 5, 1817--1840. doi:10.1214/12-AAP887. https://projecteuclid.org/euclid.aoap/1377696299


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