St. Petersburg portfolio games

László Györfi, Péter Kevei

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We investigate the performance of the constantly rebalanced portfolios, when the random vectors of the market process {Xi} are independent, and each of them distributed as (X(1), X(2), ..., X (d), 1), d ≥ 1, where X(1), X(2), ..., X(d) are nonnegative iid random variables. Under general conditions we show that the optimal strategy is the uniform: (1/d, ..., 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 ≥ 3 we prove that the uniform strategy is the best, and we obtain tight asymptotic results for the growth rate.

Original languageEnglish
Title of host publicationAlgorithmic Learning Theory - 20th International Conference, ALT 2009, Proceedings
Pages83-96
Number of pages14
DOIs
Publication statusPublished - Dec 1 2009
Event20th International Conference on Algorithmic Learning Theory, ALT 2009 - Porto, Portugal
Duration: Oct 3 2009Oct 5 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5809 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other20th International Conference on Algorithmic Learning Theory, ALT 2009
CountryPortugal
CityPorto
Period10/3/0910/5/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Györfi, L., & Kevei, P. (2009). St. Petersburg portfolio games. In Algorithmic Learning Theory - 20th International Conference, ALT 2009, Proceedings (pp. 83-96). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5809 LNAI). https://doi.org/10.1007/978-3-642-04414-4_11