Stochastic interpretation of universal portfolio and generalized target classes

Mariko Tsurusaki, Jun'Ichi Takeuchi

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

1 Citation (Scopus)

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 languageEnglish
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages390-394
Number of pages5
DOIs
Publication statusPublished - Oct 26 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: Jul 31 2011Aug 5 2011

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8104

Other

Other2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
CountryRussian Federation
CitySt. Petersburg
Period7/31/118/5/11

Fingerprint

Probability density function
Target
Latent Variables
Jeffreys Prior
Universal Cover
Latent Variable Models
Fisher Information
Regret
Hidden Markov models
Parametric Model
Random processes
Minimax
Bernoulli
Markov Model
Interpretation
Class
Stochastic Processes
Strictly
Coding
Restriction

All Science Journal Classification (ASJC) codes

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

Cite this

Tsurusaki, M., & Takeuchi, JI. (2011). Stochastic interpretation of universal portfolio and generalized target classes. In 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.

2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011. 2011. p. 390-394 6034153 (IEEE International Symposium on Information Theory - Proceedings).

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

Tsurusaki, M & Takeuchi, JI 2011, Stochastic interpretation of universal portfolio and generalized target classes. in 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
Tsurusaki M, Takeuchi JI. Stochastic interpretation of universal portfolio and generalized target classes. In 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011. 2011. p. 390-394. 6034153. (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2011.6034153
Tsurusaki, Mariko ; Takeuchi, Jun'Ichi. / Stochastic interpretation of universal portfolio and generalized target classes. 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011. 2011. pp. 390-394 (IEEE International Symposium on Information Theory - Proceedings).
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