Universal portfolios with side information

Abstract

We present a sequential investment algorithm, the-weighted universal portfolio with side-information, which a c hieves, to rst order in the exponent, the same wealth as the best side-information dependent i n v estment strategy the best state-constant re-balanced portfolio determined in hindsight from observed market and side-information outcomes. This is an individual sequence result which shows that the diierence between the exponential growth rates of wealth of the best state-constant rebalanced portfolio and the universal portfolio with side-information is uniformly less than d=2n logn + 1 + k=n log 2 for every stock market and side-information sequence and for all time n. Here d = km , 1 is the number of degrees of freedom in the state-constant rebal-anced portfolio with k states of side-information and m stocks. The proof of this result establishes a close connection between universal investment and universal data compression.

DOI: 10.1109/18.485708

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