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.

翻译：本文开发了一个二元赌博框架，用于刻画累积前景理论（CPT）中的风险敏感性与损失厌恶。所提出的概率风险敏感性度量定义为一种概率阈值比，该比值决定了在涉及确定结果与二元赌博或两个二元赌博的选择问题中的接受阈值与偏好阈值。我们展示了对称与非对称赌博厌恶的标准概念如何在此框架内被恢复，并将由此产生的阈值条件与效用溢价、概率溢价以及Arrow-Pratt曲率测度进行了比较。该分析厘清了这些准则何时一致、何时分歧，特别是在递增厌恶条件、概率分布不等的二元赌博以及涉及概率权重函数的情境下。我们还识别了当使用CPT-效用函数在参考点表示损失厌恶时所产生的技术限制。所提出的框架为风险敏感性提供了一种直接与概率阈值相关的决策理论解释，并补充了现有基于溢价的处理方法。