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Existence and Uniqueness for the Multivariate Discrete Terminal Wealth Relative

Author

Listed:
  • Andreas Hermes

    (Institute for Mathematics, RWTH Aachen University, Templergraben 55, D-52062 Aachen, Germany)

  • Stanislaus Maier-Paape

    (Institute for Mathematics, RWTH Aachen University, Templergraben 55, D-52062 Aachen, Germany)

Abstract

In this paper, the multivariate fractional trading ansatz of money management from Vince (Vince 1990) is discussed. In particular, we prove existence and uniqueness of an “optimal f ” of the respective optimization problem under reasonable assumptions on the trade return matrix. This result generalizes a similar result for the univariate fractional trading ansatz. Furthermore, our result guarantees that the multivariate optimal f solutions can always be found numerically by steepest ascent methods.

Suggested Citation

  • Andreas Hermes & Stanislaus Maier-Paape, 2017. "Existence and Uniqueness for the Multivariate Discrete Terminal Wealth Relative," Risks, MDPI, vol. 5(3), pages 1-19, August.
    • Handle: RePEc:gam:jrisks:v:5:y:2017:i:3:p:44-:d:110092
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    References listed on IDEAS

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    1. Stanislaus Maier-Paape, 2016. "Risk averse fractional trading using the current drawdown," Papers 1612.02985, arXiv.org.
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    Cited by:

    1. Stanislaus Maier-Paape & Qiji Jim Zhu, 2018. "A General Framework for Portfolio Theory. Part II: Drawdown Risk Measures," Risks, MDPI, vol. 6(3), pages 1-31, August.
    2. Stanislaus Maier-Paape & Qiji Jim Zhu, 2018. "A General Framework for Portfolio Theory—Part I: Theory and Various Models," Risks, MDPI, vol. 6(2), pages 1-35, May.

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    1. Stanislaus Maier-Paape & Qiji Jim Zhu, 2018. "A General Framework for Portfolio Theory—Part I: Theory and Various Models," Risks, MDPI, vol. 6(2), pages 1-35, May.
    2. Stanislaus Maier-Paape & Qiji Jim Zhu, 2017. "A General Framework for Portfolio Theory. Part I: theory and various models," Papers 1710.04579, arXiv.org.

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