2010/05/31 by Constantinos Kardaras, Scott Robertson · 2 citations
Economics, Econometrics and Finance · Mathematics · #q-fin.PM #math.PR
paper · pdf · doi:10.1214/11-aap802
published as Annals of Applied Probability 2012, Vol. 22, No. 4, 1576-1610 · 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)
arxiv created 2012/08/21 · arxiv updated 2012/08/22
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].