论文标题
设置价值风险措施引起的不完整偏好的多功能表示
Multi-utility representations of incomplete preferences induced by set-valued risk measures
论文作者
论文摘要
我们建立了由设定价值风险度量引起的偏好关系的多种数值表示。由于这种偏好的普遍不完整，我们必须处理多功能表示。我们寻找既是简约的表示形式（代表功能的家族由一组可拖动的参数索引）和表现良好（表示功能满足了相对于替代方案的基础空间的结构，可以满足良好的规律性属性）。我们结果的关键是统一文献中现有的双重表示的设置价值风险度量的一般双重表示，并突出了其与标量风险度量的双重性结果的联系。
We establish a variety of numerical representations of preference relations induced by set-valued risk measures. Because of the general incompleteness of such preferences, we have to deal with multi-utility representations. We look for representations that are both parsimonious (the family of representing functionals is indexed by a tractable set of parameters) and well behaved (the representing functionals satisfy nice regularity properties with respect to the structure of the underlying space of alternatives). The key to our results is a general dual representation of set-valued risk measures that unifies the existing dual representations in the literature and highlights their link with duality results for scalar risk measures.
