AI 中文总结
该研究针对风险偏好建模的广义失真风险度量，构建偏好鲁棒决策框架，通过Wasserstein距离等构造模糊集，推导闭式表达式，扩展至秩依赖效用以解决阿莱悖论。
AI 中文摘要
我们提出了一个偏好鲁棒决策框架，其中风险偏好通过广义失真风险度量建模。与分布鲁棒性不同，我们的方法解决的是风险泛函本身的模糊性问题。我们利用Wasserstein距离和Bregman散度构造失真（权重）函数的模糊集，并推导最坏情况和最好情况失真风险度量的闭式表达式。我们还将该框架扩展到秩依赖效用，得到偏好鲁棒行为模型。特别地，秩依赖效用作为期望效用模型的鲁棒化形式出现，为解决阿莱悖论提供了新方法。
英文摘要
We introduce a framework for preference-robust decision making when preferences over risk are modelled through generalised distortion risk measures. Unlike distributional robustness, our approach addresses ambiguity in the risk functional itself. We construct ambiguity sets on distortion (weight) functions using the Wasserstein distance and Bregman divergences, and derive closed-form expressions for the worst- and best-case distortion risk measures. We further extend the framework to rank-dependent utility, yielding preference-robust behavioural models. In particular, rank-dependent utility appears as a robustification of the expected utility model, yielding a novel way to address the Allais paradox.
