New stochastic dominance theory for investors with risk-averse and risk-seeking utilities with applications including solutions for the Friedman–Savage paradox

Purpose This paper introduces a novel stochastic dominance (SD) theory tailored for investors with combined risk-averse and risk-seeking utilities. It aims to address the Friedman–Savage paradox, which questions why individuals simultaneously purchase insurance and lottery tickets. Design/methodology/approach Drawing on concepts from Fishburn and Kochenberger (1979), Thon and Thorlund-Petersen (1988) and Chew and Tan (2005), we define a j-order utility framework – called AD utility – that incorporates both risk-averse and risk-seeking components. We develop an ascending-and-descending stochastic dominance (ADSD) theory to analyze the investment behavior of AD investors. Findings The ADSD theory possesses key properties such as expected utility maximization, hierarchy, transitivity and diversification, even under equal means conditions. It offers new solutions to the Friedman–Savage paradox, demonstrating that AD investors may invest in both diversified portfolios and individual assets, as well as pairs of less-risky and more-risky assets. Research limitations/implications Future research could extend the ADSD framework by exploring empirical applications and testing the theory in different market conditions. Further work is needed to refine the model's assumptions and evaluate its predictive power across various investor profiles. Practical implications ADSD theory provides a valuable framework for understanding investor behavior in real-world financial markets. It explains why investors might simultaneously choose low-risk and high-risk investments, informing portfolio management strategies and investment decision-making. Social implications This study enhances understanding of diverse investment behaviors, offering insights into financial decision-making processes. It may inform policies promoting balanced investment strategies and responsible financial planning. Originality/value This paper introduces a unique approach to SD theory by integrating risk-averse and risk-seeking utilities. The ADSD framework advances existing literature and provides a novel solution to long-standing economic paradoxes.