### Abstract

We investigate the performance of the constantly rebalanced portfolios, when the random vectors of the market process {X_{i}} 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 language | English |
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Title of host publication | Algorithmic Learning Theory - 20th International Conference, ALT 2009, Proceedings |

Pages | 83-96 |

Number of pages | 14 |

DOIs | |

Publication status | Published - Dec 1 2009 |

Event | 20th International Conference on Algorithmic Learning Theory, ALT 2009 - Porto, Portugal Duration: Oct 3 2009 → Oct 5 2009 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 5809 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 20th International Conference on Algorithmic Learning Theory, ALT 2009 |
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Country | Portugal |

City | Porto |

Period | 10/3/09 → 10/5/09 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*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