论文标题
Minkowski仪表和偏差措施
Minkowski gauges and deviation measures
论文作者
论文摘要
我们建议通过一组可接受的位置的Minkowski仪表得出偏差度量。我们表明，鉴于合适的接受集，我们的框架中可以容纳任何积极的均匀偏差措施。在这样做的过程中，我们为这种措施提供了一种新的解释，即，它们量化了人们必须缩小或将其缩小的位置缩小或将其成为可接受的位置。特别是，凸的集合的Minkowski偏差，在标量添加下稳定，并且在非稳定的径向界定是一般的偏差度量。此外，我们探讨了归因于验收集的数学和财务属性之间存在的关系，以及诱导度量的相应属性。因此，我们填补了缺乏偏差措施的接受设置的空白。提供了双极组和支持功能的双重特征。
We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that, given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In doing so, we provide a new interpretation for such measures, namely, that they quantify how much one must shrink or deleverage a position for it to become acceptable. In particular, the Minkowski Deviation of a set which is convex, stable under scalar addition, and radially bounded at non-constants, is a generalized deviation measure. Furthermore, we explore the relations existing between mathematical and financial properties attributable to an acceptance set, and the corresponding properties of the induced measure. Hence, we fill the gap that is the lack of an acceptance set for deviation measures. Dual characterizations in terms of polar sets and support functionals are provided.
