Stochastic interpretation of universal portfolio and generalized target classes

Mariko Tsurusaki, Jun'Ichi Takeuchi

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

1 被引用数 (Scopus)

抄録

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.

本文言語英語
ホスト出版物のタイトル2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
ページ390-394
ページ数5
DOI
出版ステータス出版済み - 10 26 2011
イベント2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, ロシア連邦
継続期間: 7 31 20118 5 2011

出版物シリーズ

名前IEEE International Symposium on Information Theory - Proceedings
ISSN(印刷版)2157-8104

その他

その他2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Countryロシア連邦
CitySt. Petersburg
Period7/31/118/5/11

All Science Journal Classification (ASJC) codes

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

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