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Quick Introduction into the General Framework of Portfolio Theory

Author

Listed:
  • Philipp Kreins

    (Institut für Mathematik, RWTH Aachen University, D-52062 Aachen, Germany
    These authors contributed equally to this work.)

  • Stanislaus Maier-Paape

    (Institut für Mathematik, RWTH Aachen University, D-52062 Aachen, Germany
    These authors contributed equally to this work.)

  • Qiji Jim Zhu

    (Department of Mathematics, Western Michigan University, 1903 W Michigan Ave, Kalamazoo, MI 49008-5248, USA
    These authors contributed equally to this work.)

Abstract

This survey offers a succinct overview of the General Framework of Portfolio Theory (GFPT), consolidating Markowitz portfolio theory, the growth optimal portfolio theory, and the theory of risk measures. Central to this framework is the use of convex analysis and duality, reflecting the concavity of reward functions and the convexity of risk measures due to diversification effects. Furthermore, practical considerations, such as managing multiple risks in bank balance sheets, have expanded the theory to encompass vector risk analysis. The goal of this survey is to provide readers with a concise tour of the GFPT’s key concepts and practical applications without delving into excessive technicalities. Instead, it directs interested readers to the comprehensive monograph of Maier-Paape, Júdice, Platen, and Zhu (2023) for detailed proofs and further exploration.

Suggested Citation

  • Philipp Kreins & Stanislaus Maier-Paape & Qiji Jim Zhu, 2024. "Quick Introduction into the General Framework of Portfolio Theory," Risks, MDPI, vol. 12(8), pages 1-24, August.
    • Handle: RePEc:gam:jrisks:v:12:y:2024:i:8:p:132-:d:1459347
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    References listed on IDEAS

    as
    1. Jonathan M. Borwein & Qiji J. Zhu, 2016. "A Variational Approach to Lagrange Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 727-756, December.
    2. Elyés Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued coherent risk measures," Finance and Stochastics, Springer, vol. 8(4), pages 531-552, November.
    3. repec:dau:papers:123456789/353 is not listed on IDEAS
    4. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    Full references (including those not matched with items on IDEAS)

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