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Asymptotically Optimal Portfolios

Author

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  • Farshid Jamshidian

Abstract

This paper extends to continuous time the concept of universal portfolio introduced by Cover (1991). Being a performance weighted average of constant rebalanced portfolios, the universal portfolio outperforms constant rebalanced and buy‐and‐hold portfolios exponentially over the long run. an asymptotic formula summarizing its long‐term performance is reported that supplements the one given by Cover. A criterion in terms of long‐term averages of instantaneous stock drifts and covariances is found which determines the particular form of the asymptotic growth. A formula for the expected universal wealth is given.

Suggested Citation

  • Farshid Jamshidian, 1992. "Asymptotically Optimal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 131-150, April.
  • Handle: RePEc:bla:mathfi:v:2:y:1992:i:2:p:131-150
    DOI: 10.1111/j.1467-9965.1992.tb00042.x
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    Cited by:

    1. Alex Garivaltis, 2021. "Universal Risk Budgeting," Papers 2106.10030, arXiv.org, revised Oct 2022.
    2. Yaroslav Melnyk & Frank Thomas Seifried, 2018. "Small†cost asymptotics for long†term growth rates in incomplete markets," Mathematical Finance, Wiley Blackwell, vol. 28(2), pages 668-711, April.
    3. Christa Cuchiero & Walter Schachermayer & Ting‐Kam Leonard Wong, 2019. "Cover's universal portfolio, stochastic portfolio theory, and the numéraire portfolio," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 773-803, July.
    4. Bin Li & Steven C. H. Hoi, 2012. "Online Portfolio Selection: A Survey," Papers 1212.2129, arXiv.org, revised May 2013.
    5. Donghan Kim, 2019. "Open Markets," Papers 1912.13110, arXiv.org.
    6. Christa Cuchiero & Walter Schachermayer & Ting-Kam Leonard Wong, 2016. "Cover's universal portfolio, stochastic portfolio theory and the numeraire portfolio," Papers 1611.09631, arXiv.org.
    7. Ting-Kam Leonard Wong, 2015. "Universal portfolios in stochastic portfolio theory," Papers 1510.02808, arXiv.org, revised Dec 2016.
    8. Alex Garivaltis, 2018. "Exact Replication of the Best Rebalancing Rule in Hindsight," Papers 1810.02485, arXiv.org, revised Mar 2019.
    9. Alex Garivaltis, 2018. "Multilinear Superhedging of Lookback Options," Papers 1810.02447, arXiv.org, revised Oct 2022.
    10. Gaivoronski, A & Stella, F, 2000. "Nonstationary Optimization Approach for Finding Universal Portfolios," MPRA Paper 21913, University Library of Munich, Germany.
    11. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.
    12. Gaivoronski, Alexei A. & Stella, Fabio, 2003. "On-line portfolio selection using stochastic programming," Journal of Economic Dynamics and Control, Elsevier, vol. 27(6), pages 1013-1043, April.
    13. Alex Garivaltis, 2018. "Super-Replication of the Best Pairs Trade in Hindsight," Papers 1810.02444, arXiv.org, revised Oct 2022.
    14. Alex Garivaltis, 2022. "Rational pricing of leveraged ETF expense ratios," Annals of Finance, Springer, vol. 18(3), pages 393-418, September.
    15. Ioannis Karatzas & Donghan Kim, 2021. "Open markets," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1111-1161, October.

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