Universal portfolios in stochastic portfolio theory

Preprint English OPEN
Wong, Ting-Kam Leonard (2015)
  • Subject: Quantitative Finance - Portfolio Management | Mathematics - Probability
    arxiv: Computer Science::Computational Engineering, Finance, and Science | Statistics::Other Statistics | Mathematics::Optimization and Control

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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    t→∞ t (i) Suppose π is generated by Φ. For every p ∈ Δn, the tangent vector v = (v1, . . . , vn) of Δn given by

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    Since Pt(Y ) → P(Y ) > 0 as A is a P-continuity set, the measures Pet are well defined for t sufficiently large.

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