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Existence and Uniqueness for the Multivariate Discrete Terminal Wealth Relative

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  • Andreas Hermes
  • Stanislaus Maier-Paape

Abstract

In this paper the multivariate fractional trading ansatz of money management from Ralph Vince (Portfolio Management Formulas: Mathematical Trading Methods for the Futures, Options, and Stock Markets, John Wiley & Sons, Inc., 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.

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  • Andreas Hermes & Stanislaus Maier-Paape, 2017. "Existence and Uniqueness for the Multivariate Discrete Terminal Wealth Relative," Papers 1703.00476, arXiv.org.
    • Handle: RePEc:arx:papers:1703.00476
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    File URL: http://arxiv.org/pdf/1703.00476
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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.
    3. Stanislaus Maier-Paape & Qiji Jim Zhu, 2017. "A General Framework for Portfolio Theory. Part II: drawdown risk measures," Papers 1710.04818, arXiv.org.

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