Robust maximization of asymptotic growth
Abstract
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].
Keywords
Cite
@article{arxiv.1005.3454,
title = {Robust maximization of asymptotic growth},
author = {Constantinos Kardaras and Scott Robertson},
journal= {arXiv preprint arXiv:1005.3454},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AAP802 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)