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Zbl pre05641000
Györfi, László; Kevei, Péter
St. Petersburg portfolio games. (English)
[A] Gavaldà, Ricard (ed.) et al., Algorithmic learning theory. 20th international conference, ALT 2009, Porto, Portugal, October 3--5, 2009. Proceedings. Berlin: Springer. Lecture Notes in Computer Science 5809. Lecture Notes in Artificial Intelligence, 83-96 (2009). ISBN 978-3-642-04413-7/pbk

Summary: We investigate the performance of the constantly rebalanced portfolios, when the random vectors of the market process $\{\bold{X}_{i }\}$ are independent, and each of them distributed as ($X ^{(1)}, X ^{(2)}, \dots , X ^{(d)}, 1)$, $d \geq 1$, where $X ^{(1)}, X ^{(2)}, \dots , X ^{(d)}$ are nonnegative iid random variables. \par Under general conditions we show that the optimal strategy is the uniform: $(1/d, \dots , 1/d, 0)$, at least for $d$ large enough. In case of St. Petersburg components we compute the average growth rate and the optimal strategy for $d = 1$, 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 $d \geq 3$ we prove that the uniform strategy is the best, and we obtain tight asymptotic results for the growth rate.

MSC 2000:: *91A60 Probabilistic games; gambling
91G10

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