English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We study the variability of a risk from the statistical viewpoint ofmultimodality of the conditional loss distribution given that the aggregateloss equals an exogenously provided capital. This conditional distributionserves as a building block for calculating risk allocations such as the Eulercapital allocation of Value-at-Risk. A superlevel set of this conditionaldistribution can be interpreted as a set of severe and plausible stressscenarios the given capital is supposed to cover. We show that variousdistributional properties of this conditional distribution, such as modality,dependence and tail behavior, are inherited from those of the underlying jointloss distribution. Among these properties, we find that modality of theconditional distribution is an important feature in risk assessment related tothe variety of risky scenarios likely to occur in a stressed situation. Underunimodality, we introduce a novel risk allocation method called maximumlikelihood allocation (MLA), defined as the mode of the conditionaldistribution given the total capital. Under multimodality, a single vector ofallocations can be less sound. To overcome this issue, we investigate theso-called multimodalty adjustment to increase the soundness of riskallocations. Properties of the conditional distribution, MLA and multimodalityadjustment are demonstrated in numerical experiments. In particular, we observethat negative dependence among losses typically leads to multimodality, andthus a higher multimodality adjustment can be required.

Modality for Scenario Analysis and Maximum Likelihood Allocation