Higher-order moments in portfolio selection problems: A comprehensive literature review

Markowitz’s portfolio selection model has been the biggest step-forward in financial decision making and has been the central point of research since its inception. The mean–variance model led to the foundation of the modern portfolio theory and suggested a systematic approach to study the asset allocation in view of risk-return trade-offs. The limitation of mean and variance-based portfolio optimization models to capture the real financial market behavior increased the researchers’ interest to include higher-order moments in the portfolio optimization studies. Addition of higher-order moments in the portfolio formulation augments the ability to model and analyze the effect of the asymmetrical distribution of the real-world stock data. This paper attempts to present a comprehensive review of the current state of research related to higher-order moments based portfolio selection models. We present a detailed systematic analysis of the existing literature based on the research trend over the years and various important parameters such as the higher-order moments, types and the number of objectives and constraints, investment periodicity, modeling environment, solution techniques used, and stock markets considered for the experiential study. The literature review and analysis done are used to find the research gaps and future possible research directions in the higher-order moment based portfolio selection models.