Efficient algorithms for universal portfolio defined by Markov models (情報論的学習理論と機械学習)

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We present efficient algorithms for universal portfolio which approximate Cover's minimax strategy. In the precedence research, we provided a new look at Cover's universal portfolio, where we saw wealth functions of portfolios as probability density functions (p.d.f.). In this view, log wealth ratio of a portfolio sequence is equal to coding regret of its p.d.f. with the target class consisting of the p.d.f. of constantly rebalanced portfolios (CRP). The p.d.f. of a CRP is a hidden Markov model with the restriction that the underlying Markov model is Bernoulli. Further, we considered the portfolio with a generalized target class defined by extending the underlying model to a Markov model, which we named constant Markov portfolio (CMP). We propose efficient algorithms to calculate universal portfolio strategies for CRP and CMP by using approximation formula of Bayes mixture strategy and the Baum-Welch algorithm, and evaluate their performance by experiments with synthetic and real data.
2011-06-13