论文标题
方案分析和最大似然分配的方式
Modality for Scenario Analysis and Maximum Likelihood Allocation
论文作者
论文摘要
我们从条件损失分布的多模式的统计观点中研究了风险的可变性，因为总损失等于外源提供的资本。该条件分布是计算风险分配的基础，例如欧拉资本分配价值风险。超级水平的一组条件分布可以解释为一组严重且合理的应力情景，给定的资本应该涵盖。我们表明，这种条件分布的各种分布特性，例如形式，依赖性和尾部行为，是从基础关节损失分布的遗传中继承的。在这些属性中，我们发现条件分布的方式是与在压力情况下可能发生的风险种类相关的风险评估中的重要特征。在单程性下，我们引入了一种称为最大似然分配（MLA）的新型风险分配方法，该方法定义为鉴于总资本的条件分布模式。在多模式下，单个分配向量的声音可能较小。为了克服这个问题，我们研究了所谓的多模式调整，以提高风险分配的健全性。在数值实验中证明了条件分布，MLA和多模式调整的特性。特别是，我们观察到损失之间的负依赖性通常会导致多模式，因此需要更高的多模式调整。
We study the variability of a risk from the statistical viewpoint of multimodality of the conditional loss distribution given that the aggregate loss equals an exogenously provided capital. This conditional distribution serves as a building block for calculating risk allocations such as the Euler capital allocation of Value-at-Risk. A superlevel set of this conditional distribution can be interpreted as a set of severe and plausible stress scenarios the given capital is supposed to cover. We show that various distributional properties of this conditional distribution, such as modality, dependence and tail behavior, are inherited from those of the underlying joint loss distribution. Among these properties, we find that modality of the conditional distribution is an important feature in risk assessment related to the variety of risky scenarios likely to occur in a stressed situation. Under unimodality, we introduce a novel risk allocation method called maximum likelihood allocation (MLA), defined as the mode of the conditional distribution given the total capital. Under multimodality, a single vector of allocations can be less sound. To overcome this issue, we investigate the so-called multimodalty adjustment to increase the soundness of risk allocations. Properties of the conditional distribution, MLA and multimodality adjustment are demonstrated in numerical experiments. In particular, we observe that negative dependence among losses typically leads to multimodality, and thus a higher multimodality adjustment can be required.
