构造可引出风险度量
Constructing elicitable risk measures
AI总结：
本文提出一种基于乘性评分函数构造可引出风险度量的方法，证明其性质并涵盖已知度量，同时支持构造新度量及高阶可引出性。
摘要：
我们提供了一种构造性的方法来定义新的可引出风险度量，这些度量由乘性评分函数刻画。我们证明，根据评分函数分量的选择，所得的风险度量具有单调性、平移不变性、凸性和正齐次性等性质。我们的框架涵盖了大多数著名的可引出风险度量，包括所有可引出的凸风险度量与一致风险度量。此外，我们的设定允许构造新的可引出风险度量，例如凸但非一致的风险度量。我们还讨论了高阶可引出性（如联合引出均值与方差或不同分位数水平）如何纳入我们的设定中。
英文摘要：
We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure possesses properties such as monotonicity, translation invariance, convexity, and positive homogeneity. Our framework encompasses the majority of well-known elicitable risk measures including all elicitable convex and coherent risk measures. Our setting moreover allows to construct novel elicitable risk measures that are, for example, convex but not coherent. Furthermore, we discuss how higher-order elicitability, such as jointly eliciting the mean and variance or different quantile levels, fall within our setting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
