Consider a family of portfolio strategies with the aim of achieving the asymptotic growth rate of the best one.  Cover's solution is to build a wealth-weighted average which can be regarded as a buy-and-hold portfolio of portfolios. When an optimal portfolio exists, the wealth-weighted average converges to it by concentration of wealth. Under suitable conditions , we show  that the distribution of wealth in the family satisfies a pathwise large deviation principle as time tends to infinity. In particular, we study Cover's portfolio for the nonparametric family of functionally generated portfolios in stochastic portfolio theory and establish its asymptotic universality.
Consider a family of portfolio strategies with the aim of achieving the asymptotic growth rate of the best one. The idea behind Cover's universal portfolio is to build a wealth-weighted average which can be viewed as a buy-and-hold portfolio of portfolios. When an optimal portfolio exists, the wealth-weighted average converges to it by concentration of wealth. Working under a discrete time and pathwise setup , we show under suitable conditions that the distribution of wealth in the family satisfies a pathwise large deviation principle as time tends to infinity. Our main result extends Cover's portfolio to the nonparametric family of functionally generated portfolios in stochastic portfolio theory and establishes its asymptotic universality.
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Working under a discrete time and pathwise setup
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under suitable conditions
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