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
T2 - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Y2 - 31 July 2011 through 5 August 2011
ER -