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 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Information Systems
- Modelling and Simulation
- Applied Mathematics
Cite this
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 proceeding › Conference contribution
}
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.
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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 -