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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
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    References listed on IDEAS

    as
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