凸不精确预测的基本问题及其应用
Convex Imprecise Previsions: Basic Issues and Applications
摘要：
在本文中，我们研究了两类不精确预测，我们称之为凸和中心凸预测，在瓦利的不精确预测理论的框架。我们发现，凸预测与凸自然延伸的概念，这是有用的纠正一大类不一致的不精确的概率评估。这一类的特点是避免无限确定损失的条件。凸性进一步为一些不确定性模型和设备提供了概念框架，如非归一化上确界保持函数。中心凸预测是介于相干预测和避免确定损失的预测之间的中间，并且它们不需要正均匀性是潜在应用的相关特征。最后，我们将展示这些概念如何应用于（金融）风险度量。
英文摘要：
In this paper we study two classes of imprecise previsions, which we termed convex and centered convex previsions, in the framework of Walley's theory of imprecise previsions. We show that convex previsions are related with a concept of convex natural estension, which is useful in correcting a large class of inconsistent imprecise probability assessments. This class is characterised by a condition of avoiding unbounded sure loss. Convexity further provides a conceptual framework for some uncertainty models and devices, like unnormalised supremum preserving functions. Centered convex previsions are intermediate between coherent previsions and previsions avoiding sure loss, and their not requiring positive homogeneity is a relevant feature for potential applications. Finally, we show how these concepts can be applied in (financial) risk measurement.
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