Gavaldà, Ricard (ed.) et al., Algorithmic learning theory. 20th international conference, ALT 2009, Porto, Portugal, October 3–5, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-04413-7/pbk). Lecture Notes in Computer Science 5809. Lecture Notes in Artificial Intelligence, 83-96 (2009).
Summary: We investigate the performance of the constantly rebalanced portfolios, when the random vectors of the market process are independent, and each of them distributed as (, , where are nonnegative iid random variables.
Under general conditions we show that the optimal strategy is the uniform: , at least for large enough. In case of St. Petersburg components we compute the average growth rate and the optimal strategy for , 2. In order to make the problem non-trivial, a commission factor is introduced and tuned to result in zero growth rate on any individual St. Petersburg components. One of the interesting observations made is that a combination of two components of zero growth can result in a strictly positive growth. For we prove that the uniform strategy is the best, and we obtain tight asymptotic results for the growth rate.