IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v7y2019i2p60-d236355.html
   My bibliography  Save this article

A General Framework for Portfolio Theory. Part III: Multi-Period Markets and Modular Approach

Author

Listed:
  • Stanislaus Maier-Paape

    (Institut für Mathematik, RWTH Aachen University, D-52062 Aachen, Germany)

  • Andreas Platen

    (Institut für Mathematik, RWTH Aachen University, D-52062 Aachen, Germany)

  • Qiji Jim Zhu

    (Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA)

Abstract

This is Part III of a series of papers which focus on a general framework for portfolio theory. Here, we extend a general framework for portfolio theory in a one-period financial market as introduced in Part I [Maier-Paape and Zhu, Risks 2018, 6(2), 53] to multi-period markets. This extension is reasonable for applications. More importantly, we take a new approach, the “modular portfolio theory”, which is built from the interaction among four related modules: (a) multi period market model; (b) trading strategies; (c) risk and utility functions (performance criteria); and (d) the optimization problem (efficient frontier and efficient portfolio). An important concept that allows dealing with the more general framework discussed here is a trading strategy generating function. This concept limits the discussion to a special class of manageable trading strategies, which is still wide enough to cover many frequently used trading strategies, for instance “constant weight” (fixed fraction). As application, we discuss the utility function of compounded return and the risk measure of relative log drawdowns.

Suggested Citation

  • Stanislaus Maier-Paape & Andreas Platen & Qiji Jim Zhu, 2019. "A General Framework for Portfolio Theory. Part III: Multi-Period Markets and Modular Approach," Risks, MDPI, vol. 7(2), pages 1-31, June.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:60-:d:236355
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/7/2/60/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/7/2/60/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Vladimir Cherny & Jan Obłój, 2013. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Finance and Stochastics, Springer, vol. 17(4), pages 771-800, October.
    3. 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.
    4. Zabarankin, Michael & Pavlikov, Konstantin & Uryasev, Stan, 2014. "Capital Asset Pricing Model (CAPM) with drawdown measure," European Journal of Operational Research, Elsevier, vol. 234(2), pages 508-517.
    5. Li, Jinfang, 2014. "Multi-period sentiment asset pricing model with information," International Review of Economics & Finance, Elsevier, vol. 34(C), pages 118-130.
    6. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    7. Yang, Chunpeng & Li, Jinfang, 2014. "Two-period trading sentiment asset pricing model with information," Economic Modelling, Elsevier, vol. 36(C), pages 1-7.
    8. Sanford J. Grossman & Zhongquan Zhou, 1993. "Optimal Investment Strategies For Controlling Drawdowns," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 241-276, July.
    9. Lisa R. Goldberg & Ola Mahmoud, 2014. "Drawdown: From Practice to Theory and Back Again," Papers 1404.7493, arXiv.org, revised Sep 2016.
    10. 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.
    11. Vladimir Cherny & Jan Obloj, 2011. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Papers 1110.6289, arXiv.org, revised Apr 2013.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leonie Violetta Brinker, 2021. "Minimal Expected Time in Drawdown through Investment for an Insurance Diffusion Model," Risks, MDPI, vol. 9(1), pages 1-18, January.
    2. David E. Allen & Michael McAleer & Shelton Peiris & Abhay K. Singh, 2014. "Hedge Fund Portfolio Diversification Strategies across the GFC," Tinbergen Institute Discussion Papers 14-151/III, Tinbergen Institute.
    3. 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.
    4. Paolo Guasoni & Jan Obłój, 2016. "The Incentives Of Hedge Fund Fees And High-Water Marks," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 269-295, April.
    5. David E. Allen & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2015. "Down-side Risk Metrics as Portfolio Diversification Strategies across the GFC," Documentos de Trabajo del ICAE 2015-19, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    6. Wang, Wenyuan & Chen, Ping & Li, Shuanming, 2020. "Generalized expected discounted penalty function at general drawdown for Lévy risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 12-25.
    7. Ola Mahmoud, 2015. "The Temporal Dimension of Risk," Papers 1501.01573, arXiv.org, revised Jun 2016.
    8. Sagara Dewasurendra & Pedro Judice & Qiji Zhu, 2019. "The Optimum Leverage Level of the Banking Sector," Risks, MDPI, vol. 7(2), pages 1-30, May.
    9. David E. Allen & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2014. "European Market Portfolio Diversifcation Strategies across the GFC," Working Papers in Economics 14/25, University of Canterbury, Department of Economics and Finance.
    10. Ankush Agarwal & Ronnie Sircar, 2017. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Working Papers hal-01388399, HAL.
    11. Dong, Yang & Wen, Shu-hui & Hu, Xiao-bing & Li, Jiang-Cheng, 2020. "Stochastic resonance of drawdown risk in energy market prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    12. Zabarankin, Michael & Pavlikov, Konstantin & Uryasev, Stan, 2014. "Capital Asset Pricing Model (CAPM) with drawdown measure," European Journal of Operational Research, Elsevier, vol. 234(2), pages 508-517.
    13. Zhang, Gongqiu & Li, Lingfei, 2023. "A general method for analysis and valuation of drawdown risk," Journal of Economic Dynamics and Control, Elsevier, vol. 152(C).
    14. Philipp M. Möller, 2018. "Drawdown Measures And Return Moments," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-42, November.
    15. Chen, Xinfu & Landriault, David & Li, Bin & Li, Dongchen, 2015. "On minimizing drawdown risks of lifetime investments," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 46-54.
    16. Landriault, David & Li, Bin & Li, Shu, 2015. "Analysis of a drawdown-based regime-switching Lévy insurance model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 98-107.
    17. Bogdan Grechuk & Michael Zabarankin, 2017. "Synergy effect of cooperative investment," Annals of Operations Research, Springer, vol. 249(1), pages 409-431, February.
    18. Ankush Agarwal & Ronnie Sircar, 2016. "Portfolio Benchmarking under Drawdown Constraint and Stochastic Sharpe Ratio," Papers 1610.08558, arXiv.org.
    19. David E. Allen & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2016. "Down-Side Risk Metrics as Portfolio Diversification Strategies across the Global Financial Crisis," JRFM, MDPI, vol. 9(2), pages 1-18, June.
    20. David Landriault & Bin Li & Hongzhong Zhang, 2017. "A Unified Approach for Drawdown (Drawup) of Time-Homogeneous Markov Processes," Papers 1702.07786, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:60-:d:236355. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.