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Description

We discuss Cover\'s universal portfolios in the context of Stochastic Portfolio Theory. By enlarging the class of portfolio generating functions, we see universal portfolios are generated by functions, given excess growth rates of constant rebalanced portfolios. These generating functions and resulting universal portfolios can be represented as integrations with respect to tilted version of maximal entropy measure. In this way we may answer one of the open questions posed by Fernholz & Karatzas (2009). With analyses of concentration of measures we evaluate performance of universal portfolios. Finally, we discuss universal portfolios under large equity market models.