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

The field of risk theory has traditionally focused on ruin-relatedquantities. In particular, the socalled Expected Discounted Penalty Functionhas been the object of a thorough study over the years. Although interesting intheir own right, ruin related quantities do not seem to capture path-dependentproperties of the reserve. In this article we aim at presenting theprobabilistic properties of drawdowns and the speed at which an insurancereserve depletes as a consequence of the risk exposure of the company. Thesenew quantities are not ruin related yet they capture important features of aninsurance position and we believe it can lead to the design of a meaningfulrisk measures. Studying drawdowns and speed of depletion for L\'evy insurancerisk processes represent a novel and challenging concept in insurancemathematics. In this paper, all these concepts are formally introduced in aninsurance setting. Moreover, using recent results in fluctuation theory forL\'evy processes, we derive expressions for the distribution of severalquantities related to the depletion problem. Of particular interest are thedistribution of drawdowns and the Laplace transform for the speed of depletion.These expressions are given for some examples of L\'evy insurance riskprocesses for which they can be calculated, in particular for the classicalCramer-Lundberg model.

On the Depletion Problem for an Insurance Risk Process: New Non-ruin Quantities in Collective Risk Theory