Weight functions and log-optimal investment portfolios
Probability
2015-10-12 v2
Abstract
Following the paper by Algoet--Cover (1988), we analyse log-optimal portfolios where return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, logarithmic growth rate is a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting; it does not depend on the form of the weight function, although the optimal rate does. The existence of an optimal investment strategy has been established earlier in a great generality by Kramkov--Schachermayer (2003) although our underlying assumptions are different.
Keywords
Cite
@article{arxiv.1505.01437,
title = {Weight functions and log-optimal investment portfolios},
author = {Y. Suhov and I. Stuhl and M. Kelbert},
journal= {arXiv preprint arXiv:1505.01437},
year = {2015}
}