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

Symeon Vaidanis; Marios Kountouris

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arXiv · 2607.22085

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

Symeon Vaidanis·Marios Kountouris

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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.

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q-fin.MF cs.CE cs.IT cs.NI math.IT

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Symeon Vaidanis, Marios Kountouris. 2026-07-24. Neilson's Weak vs. Strong Loss Aversion: A Characterization and a Generalized CPT-Utility Function. https://arxiv.org/abs/2607.22085

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