The Annals of Applied Probability

Robust maximization of asymptotic growth

Constantinos Kardaras and Scott Robertson

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This paper addresses the question of how to invest in a robust growth-optimal way in a market where the instantaneous expected return of the underlying process is unknown. The optimal investment strategy is identified using a generalized version of the principal eigenfunction for an elliptic second-order differential operator, which depends on the covariance structure of the underlying process used for investing. The robust growth-optimal strategy can also be seen as a limit, as the terminal date goes to infinity, of optimal arbitrages in the terminology of Fernholz and Karatzas [Ann. Appl. Probab. 20 (2010) 1179–1204].

Article information

Ann. Appl. Probab., Volume 22, Number 4 (2012), 1576-1610.

First available in Project Euclid: 10 August 2012

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Zentralblatt MATH identifier

Primary: 60G44: Martingales with continuous parameter 60G46: Martingales and classical analysis 60H05: Stochastic integrals

Asymptotic growth rate robustness generalized martingale problem optimal arbitrage


Kardaras, Constantinos; Robertson, Scott. Robust maximization of asymptotic growth. Ann. Appl. Probab. 22 (2012), no. 4, 1576--1610. doi:10.1214/11-AAP802.

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