### Abstract

In this paper, we consider the sequential portfolio investment problem considered by Cover [3] and extend the results of [3] to the class of piecewise constant rebalanced portfolios that are tuned to the underlying sequence of price relatives. Here, the piecewise constant models are used to partition the space of past price relative vectors where we assign a different constant rebalanced portfolio to each region independently. We then extend these results where we compete against a doubly exponential number of piecewise constant portfolios that are represented by a context tree. We use the context tree to achieve the wealth of a portfolio selection algorithm that can choose both its partitioning of the space of the past price relatives and its constant rebalanced portfolio within each region of the partition, based on observing the entire sequence of price relatives in advance, uniformly, for every bounded deterministic sequence of price relative vectors. This performance is achieved with a portfolio algorithm whose complexity is only linear in the depth of the context tree per investment period. We demonstrate that the resulting portfolio algorithm achieves significant gains on historical stock pairs over the algorithm of [3] and the best constant rebalanced portfolio.

Original language | English (US) |
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Title of host publication | 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP |

Pages | 2093-2096 |

Number of pages | 4 |

DOIs | |

State | Published - Sep 16 2008 |

Event | 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP - Las Vegas, NV, United States Duration: Mar 31 2008 → Apr 4 2008 |

### Publication series

Name | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
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ISSN (Print) | 1520-6149 |

### Other

Other | 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP |
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Country | United States |

City | Las Vegas, NV |

Period | 3/31/08 → 4/4/08 |

### Fingerprint

### Keywords

- Context tree
- Investment
- Piecewise models
- Portfolio
- Universal

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Signal Processing
- Acoustics and Ultrasonics

### Cite this

*2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP*(pp. 2093-2096). [4518054] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2008.4518054

**Universal portfolios via context trees.** / Kozat, Suleyman S.; Singer, Andrew Carl; Bean, Andrew J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP.*, 4518054, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, pp. 2093-2096, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP, Las Vegas, NV, United States, 3/31/08. https://doi.org/10.1109/ICASSP.2008.4518054

}

TY - GEN

T1 - Universal portfolios via context trees

AU - Kozat, Suleyman S.

AU - Singer, Andrew Carl

AU - Bean, Andrew J.

PY - 2008/9/16

Y1 - 2008/9/16

N2 - In this paper, we consider the sequential portfolio investment problem considered by Cover [3] and extend the results of [3] to the class of piecewise constant rebalanced portfolios that are tuned to the underlying sequence of price relatives. Here, the piecewise constant models are used to partition the space of past price relative vectors where we assign a different constant rebalanced portfolio to each region independently. We then extend these results where we compete against a doubly exponential number of piecewise constant portfolios that are represented by a context tree. We use the context tree to achieve the wealth of a portfolio selection algorithm that can choose both its partitioning of the space of the past price relatives and its constant rebalanced portfolio within each region of the partition, based on observing the entire sequence of price relatives in advance, uniformly, for every bounded deterministic sequence of price relative vectors. This performance is achieved with a portfolio algorithm whose complexity is only linear in the depth of the context tree per investment period. We demonstrate that the resulting portfolio algorithm achieves significant gains on historical stock pairs over the algorithm of [3] and the best constant rebalanced portfolio.

AB - In this paper, we consider the sequential portfolio investment problem considered by Cover [3] and extend the results of [3] to the class of piecewise constant rebalanced portfolios that are tuned to the underlying sequence of price relatives. Here, the piecewise constant models are used to partition the space of past price relative vectors where we assign a different constant rebalanced portfolio to each region independently. We then extend these results where we compete against a doubly exponential number of piecewise constant portfolios that are represented by a context tree. We use the context tree to achieve the wealth of a portfolio selection algorithm that can choose both its partitioning of the space of the past price relatives and its constant rebalanced portfolio within each region of the partition, based on observing the entire sequence of price relatives in advance, uniformly, for every bounded deterministic sequence of price relative vectors. This performance is achieved with a portfolio algorithm whose complexity is only linear in the depth of the context tree per investment period. We demonstrate that the resulting portfolio algorithm achieves significant gains on historical stock pairs over the algorithm of [3] and the best constant rebalanced portfolio.

KW - Context tree

KW - Investment

KW - Piecewise models

KW - Portfolio

KW - Universal

UR - http://www.scopus.com/inward/record.url?scp=51449083099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51449083099&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2008.4518054

DO - 10.1109/ICASSP.2008.4518054

M3 - Conference contribution

AN - SCOPUS:51449083099

SN - 1424414849

SN - 9781424414840

T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

SP - 2093

EP - 2096

BT - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP

ER -