Neilson's Weak vs. Strong Loss Aversion: A Characterization and a Generalized CPT-Utility Function

2026-07-24

AI Summary

This study addresses the limitations of traditional expected utility theory in capturing individuals’ subjective sensitivity to losses and the structural constraints inherent in standard cumulative prospect theory (CPT) when satisfying Neilson’s loss aversion conditions. By employing a game-theoretic interpretation, the paper clarifies the conceptual distinction between Neilson’s weak and strong notions of loss aversion, delineating their equivalence and divergence conditions. To overcome the rigidity of canonical CPT utility representations—such as those by Köbberling and Wakker—the work proposes a generalized CPT utility function that preserves reference dependence while offering greater flexibility. This new formulation admits an explicit analytical expression, uniquely balancing behavioral plausibility with mathematical tractability. It enables sensitivity analysis and optimization applications, thereby extending CPT’s descriptive scope and providing both a theoretical foundation and a practical tool for modeling decision-making under Neilson’s loss aversion criteria.

Abstract

In multi-objective and multi-criteria decision-making under risk, especially in settings involving individual behavior, risk-aware analysis based on subjective evaluation has become increasingly important. Moving beyond risk-neutral modeling and the constraints of Expected Utility Theory (EUT), Cumulative Prospect Theory (CPT) provides a behaviorally grounded framework for capturing how individuals perceive and evaluate risky prospects. This paper conducts a rigorous theoretical analysis of Neilson's definitions of aversion. We provide a gamble-based interpretation, sharpen key conceptual distinctions, and make explicit the conditions under which the weak and strong notions coincide as well as when they diverge. Furthermore, we examine the Kobberling-Wakker utility function and related standard CPT specifications, highlighting structural limitations and inconsistencies that arise when these forms are required to satisfy Neilson-type aversion conditions. To address these issues, we propose a generalized CPT-utility function that retains the canonical reference-dependent shape while offering additional flexibility. This generalization extends the descriptive scope of CPT and provides an explicit functional form that is useful for sensitivity analysis and utility function-based optimization.

Problem

• loss aversion
• Cumulative Prospect Theory
• utility function
• risk preference
• behavioral decision-making

Innovation

• Cumulative Prospect Theory
• loss aversion
• generalized utility function
• reference dependence
• risk-sensitive decision-making