Probabilistic Risk Sensitivity and Loss Aversion in Cumulative Prospect Theory

2026-06-04

AI Summary

This study addresses the quantification of risk sensitivity and loss aversion within Cumulative Prospect Theory (CPT) and clarifies their relationship with classical risk measures. By constructing a binary gamble framework, the authors characterize the preference boundary between certain outcomes and risky prospects using a probability threshold ratio, thereby proposing a novel measure of risk sensitivity grounded in this threshold. The approach elucidates both connections and distinctions with established criteria such as utility premium, probability premium, and Arrow–Pratt curvature, while also identifying the technical constraints imposed by loss aversion at the reference point in CPT. The work unifies and extends conditions for symmetric and asymmetric bet aversion, establishing an interpretable and operational framework for analyzing risk sensitivity and delineating the domains of applicability for various risk measurement criteria.

Abstract

This paper develops a binary-gamble framework for characterizing risk sensitivity and loss aversion in Cumulative Prospect Theory (CPT). The proposed probabilistic risk-sensitivity metric is defined as a probability-threshold ratio that determines acceptance and preference thresholds in choice problems involving either a certain outcome and a binary gamble or two binary gambles. We show how standard notions of symmetric and non-symmetric bet aversion can be recovered within this framework, and we compare the resulting threshold-based conditions with utility premia, probability premia, and Arrow--Pratt curvature measures. The analysis clarifies when these criteria coincide and when they diverge, particularly for increasing aversion conditions, binary gambles with unequal probability distributions, and settings involving probability weighting functions. We also identify technical restrictions that arise when CPT-utility functions are used to represent loss aversion at the reference point. The resulting framework provides a decision-theoretic interpretation of risk sensitivity that is directly tied to probability thresholds and complements existing premium-based approaches.

Problem

• risk sensitivity
• loss aversion
• Cumulative Prospect Theory
• probability threshold
• binary gamble

Innovation

• Cumulative Prospect Theory
• risk sensitivity
• loss aversion
• probability threshold
• binary gamble