Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/258141 
Year of Publication: 
2021
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 9 [Issue:] 3 [Article No.:] 52 [Publisher:] MDPI [Place:] Basel [Year:] 2021 [Pages:] 1-38
Publisher: 
MDPI, Basel
Abstract: 
The aim of this paper is to merge order statistics with natural catastrophe reinsurance pricing to develop new theoretical and practical insights relevant to market practice and model development. We present a novel framework to quantify the role that occurrence losses (order statistics) play in pricing of catastrophe excess of loss (catXL) contracts. Our framework enables one to analytically quantify the contribution of a given occurrence loss to the mean and covariance structure, before and after the application of a catXL contract. We demonstrate the utility of our framework with an application to idealized catastrophe models for a multi-peril and a hurricane-only case. For the multi-peril case, we show precisely how contributions to so-called lower layers are dominated by high frequency perils, whereas higher layers are dominated by low-frequency high severity perils. Our framework enables market practitioners and model developers to assess and understand the impact of altered model assumptions on the role of occurrence losses in catXL pricing.
Subjects: 
catastrophe risk modeling
catXL pricing
occurrence losses
order statistics
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
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