Next Article in Journal
The Investigation of a Forward-Rate Mortality Framework
Next Article in Special Issue
Market-Risk Optimization among the Developed and Emerging Markets with CVaR Measure and Copula Simulation
Previous Article in Journal
American Options on High Dividend Securities: A Numerical Investigation
Previous Article in Special Issue
Statistical Inference for the Beta Coefficient
Open AccessArticle

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

1
Institut für Mathematik, RWTH Aachen University, D-52062 Aachen, Germany
2
Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA
*
Author to whom correspondence should be addressed.
Risks 2019, 7(2), 60; https://doi.org/10.3390/risks7020060
Received: 6 May 2019 / Revised: 25 May 2019 / Accepted: 27 May 2019 / Published: 1 June 2019
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. View Full-Text
Keywords: portfolio theory; modular portfolio theory; efficient frontier; trading strategy; multi-period market model; arbitrage; bond replicating; risk-free; relative log drawdown portfolio theory; modular portfolio theory; efficient frontier; trading strategy; multi-period market model; arbitrage; bond replicating; risk-free; relative log drawdown
Show Figures

Figure 1

MDPI and ACS Style

Maier-Paape, S.; Platen, A.; Zhu, Q.J. A General Framework for Portfolio Theory. Part III: Multi-Period Markets and Modular Approach. Risks 2019, 7, 60.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop