Quick Introduction into the General Framework of Portfolio Theory

Risks, vol. 12, pp. 132

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.

Authors 3

1. Philipp Kreins corresponding Aachen Institut für Mathematik

   RWTH Aachen University

   Affiliation as printed

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

2. Stanislaus Maier‐Paape Aachen Institut für Mathematik

   RWTH Aachen University

   Affiliation as printed

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

3. Qiji Jim Zhu

   Western Michigan University

   Affiliation as printed

   Department of Mathematics, Western Michigan University, 1903 W Michigan Ave, Kalamazoo, MI 49008-5248, USA