Quick Introduction into the General Framework of Portfolio Theory

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