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arXiv · 1505.01437

Weight functions and log-optimal investment portfolios

Y. Suhov·I. Stuhl·M. Kelbert
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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.

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Y. Suhov, I. Stuhl, M. Kelbert. 2015-05-06. Weight functions and log-optimal investment portfolios. https://arxiv.org/abs/1505.01437

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