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Universal portfolios in stochastic portfolio theory

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  • Ting-Kam Leonard Wong

Abstract

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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  • Ting-Kam Leonard Wong, 2015. "Universal portfolios in stochastic portfolio theory," Papers 1510.02808, arXiv.org, revised Dec 2016.
    • Handle: RePEc:arx:papers:1510.02808
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    4. Jason E. Cross & Andrew R. Barron, 2003. "Efficient Universal Portfolios for Past‐Dependent Target Classes," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 245-276, April.
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    7. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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