Universal portfolios in stochastic portfolio theory

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Wong, Ting-Kam Leonard;
  • 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 optim... View more
  • References (27)
    27 references, page 1 of 3

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

    for all open sets G such that G ∩ supp(ν0) 6= ∅. These inequalities and Lemma 4.11 imply the LDP.

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

    We claim that Pet converges weakly to Pe. This implies the statement because f is bounded continuous on Y and Z 1 Z 1 Z Z To prove the claim, it suffices by the Portmanteau theorem to show that Pet(A) → 1

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