Quick Introduction into the General Framework of Portfolio Theory

Philipp Kreins (), Stanislaus Maier-Paape and Qiji Jim Zhu
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Philipp Kreins: Institut für Mathematik, RWTH Aachen University, D-52062 Aachen, Germany
Stanislaus Maier-Paape: Institut für Mathematik, RWTH Aachen University, D-52062 Aachen, Germany
Qiji Jim Zhu: Department of Mathematics, Western Michigan University, 1903 W Michigan Ave, Kalamazoo, MI 49008-5248, USA

Risks, 2024, vol. 12, issue 8, 1-24

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.

Keywords: general framework of portfolio theory; convex programming; financial mathematics; risk measures; utility functions; efficient frontier; Markowitz portfolio theory; capital market asset pricing model; growth optimal portfolio; fractional Kelly allocation (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2024
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