### Abstract

We provide a new look at Cover's universal portfolio, where we define probability density functions (p.d.f.) representing wealth functions of portfolios. In this view, log wealth ratio of a portfolio sequence is equal to coding regret of its p.d.f. for the target class which consists of the p.d.f. representing constantly rebalanced portfolios (CRP). It is revealed that the p.d.f. of a CRP is a hidden Markov model (HMM) with the restriction that the latent variable's distribution is Bernoulli. Further we consider the portfolio with the generalized target class defined by extending the latent variable's distribution to a parametric model of stochastic processes. Then, we discuss the minimax log wealth ratio of the class analyzing Fisher information of the p.d.f. for portfolios, which is strictly smaller than that of the latent variable's model. Finally we propose a portfolio strategy using the Jeffreys prior of the class of p.d.f. and an efficient method to calculate causal portfolios using the Baum-Welch algorithm.

Original language | English |
---|---|

Title of host publication | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 |

Pages | 390-394 |

Number of pages | 5 |

DOIs | |

Publication status | Published - Oct 26 2011 |

Event | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation Duration: Jul 31 2011 → Aug 5 2011 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
---|---|

ISSN (Print) | 2157-8104 |

### Other

Other | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 |
---|---|

Country | Russian Federation |

City | St. Petersburg |

Period | 7/31/11 → 8/5/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modelling and Simulation
- Applied Mathematics

### Cite this

*2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011*(pp. 390-394). [6034153] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2011.6034153

**Stochastic interpretation of universal portfolio and generalized target classes.** / Tsurusaki, Mariko; Takeuchi, Jun'Ichi.

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

*2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011.*, 6034153, IEEE International Symposium on Information Theory - Proceedings, pp. 390-394, 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011, St. Petersburg, Russian Federation, 7/31/11. https://doi.org/10.1109/ISIT.2011.6034153

}

TY - GEN

T1 - Stochastic interpretation of universal portfolio and generalized target classes

AU - Tsurusaki, Mariko

AU - Takeuchi, Jun'Ichi

PY - 2011/10/26

Y1 - 2011/10/26

N2 - We provide a new look at Cover's universal portfolio, where we define probability density functions (p.d.f.) representing wealth functions of portfolios. In this view, log wealth ratio of a portfolio sequence is equal to coding regret of its p.d.f. for the target class which consists of the p.d.f. representing constantly rebalanced portfolios (CRP). It is revealed that the p.d.f. of a CRP is a hidden Markov model (HMM) with the restriction that the latent variable's distribution is Bernoulli. Further we consider the portfolio with the generalized target class defined by extending the latent variable's distribution to a parametric model of stochastic processes. Then, we discuss the minimax log wealth ratio of the class analyzing Fisher information of the p.d.f. for portfolios, which is strictly smaller than that of the latent variable's model. Finally we propose a portfolio strategy using the Jeffreys prior of the class of p.d.f. and an efficient method to calculate causal portfolios using the Baum-Welch algorithm.

AB - We provide a new look at Cover's universal portfolio, where we define probability density functions (p.d.f.) representing wealth functions of portfolios. In this view, log wealth ratio of a portfolio sequence is equal to coding regret of its p.d.f. for the target class which consists of the p.d.f. representing constantly rebalanced portfolios (CRP). It is revealed that the p.d.f. of a CRP is a hidden Markov model (HMM) with the restriction that the latent variable's distribution is Bernoulli. Further we consider the portfolio with the generalized target class defined by extending the latent variable's distribution to a parametric model of stochastic processes. Then, we discuss the minimax log wealth ratio of the class analyzing Fisher information of the p.d.f. for portfolios, which is strictly smaller than that of the latent variable's model. Finally we propose a portfolio strategy using the Jeffreys prior of the class of p.d.f. and an efficient method to calculate causal portfolios using the Baum-Welch algorithm.

UR - http://www.scopus.com/inward/record.url?scp=80054795049&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054795049&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2011.6034153

DO - 10.1109/ISIT.2011.6034153

M3 - Conference contribution

AN - SCOPUS:80054795049

SN - 9781457705953

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 390

EP - 394

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

ER -