Concave/convex weighting and utility functions for risk: A new light on classical theorems
分析了风险决策中凹/凸效用函数和概率扭曲函数的特征，通过偏好凸性条件刻画了几乎所有现有模型，无需预设连续性或可微性，并揭示了Yaari对偶理论中概率混合与结果混合凸性等价的新发现。
This paper analyzes concave and convex utility and probability distortion functions for decision under risk (law-invariant functionals). We characterize concave utility for virtually all existing models, and concave/convex probability distortion functions for rank-dependent utility and prospect theory in complete generality, through an appealing and well-known condition (convexity of preference, i.e., quasiconcavity of the functional). Unlike preceding results, we do not need to presuppose any continuity, let be differentiability. An example of a new light shed on classical results: whereas, in general, convexity/concavity with respect to probability mixing is mathematically distinct from convexity/concavity with respect to outcome mixing, in Yaari's dual theory (i.e., Wang's premium principle) these conditions are not only dual, as was well-known, but also logically equivalent, which had not been known before.