Probabilistic Risk Sensitivity and Loss Aversion in Cumulative Prospect Theory
For decision theorists and behavioral economists, this provides a new decision-theoretic interpretation of risk sensitivity tied to probability thresholds, complementing existing approaches.
The paper develops a binary-gamble framework for characterizing risk sensitivity and loss aversion in Cumulative Prospect Theory, introducing a probabilistic risk-sensitivity metric based on probability-threshold ratios. It clarifies when standard criteria coincide or diverge, particularly for increasing aversion and unequal probability distributions.
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.