Portfolio Selection and Online Learning

This paper studies a new strategy for selecting portfolios in the stock market. The strategy is inspired by two streams of previous work: (1) work on universalization of strategies for portfolio selection, which began with Thomas Cover's work on constant rebalanced portfolios, published in 1991, 4 and (2) more general work on universalization of online algorithms, 17,21,23,30 especially Vladimir Vovk's work on the aggregating algorithm and Markov switching strategies. 32 The proposed investment strategy achieves asymptotically the same exponential rate of growth as the portfolio that turns out to be best expost in the long run and does not require any underlying statistical assumptions on the nature of the stock market.