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

Stanislaus Maier-Paape, Andreas Platen and Qiji Jim Zhu
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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

Risks, 2019, vol. 7, issue 2, 1-31

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.

Keywords: portfolio theory; modular portfolio theory; efficient frontier; trading strategy; multi-period market model; arbitrage; bond replicating; risk-free; relative log drawdown (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2019
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