Portfolio risk analysis of excess of loss reinsurance

Qihe Tang, Zhiwei Tong and Li Xun

Insurance: Mathematics and Economics, 2022, vol. 102, issue C, 91-110

Abstract: Consider a catastrophe insurance market in which primary insurers purchase excess of loss reinsurance to transfer their higher-layer losses to a reinsurer. We conduct a portfolio risk analysis for the reinsurer. In doing so, we model the losses to the primary insurers by a mixture structure, which effectively integrates three risk factors: common shock, systematic risk, and idiosyncratic risk. Assume that the reinsurer holds an initial capital Cn that is in accordance with its market size n. When expanding its business, the reinsurer needs to comply with a certain VaR-based solvency capital requirement, which determines an infimal retention level rn according to the initial capital Cn. As our main results, we find the limit of rn as n→∞ and then establish a weak convergence for the reinsurance portfolio loss. The latter result is applied to approximate the distortion risk measures of the reinsurance portfolio loss. In our numerical studies, we examine the accuracy of the obtained approximations and conduct various sensitivity tests against some risk parameters.

Keywords: Mixture; Solvency capital requirement; Retention; Law of large numbers; Distortion risk measures (search for similar items in EconPapers)
JEL-codes: G22 G32 G33 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:102:y:2022:i:c:p:91-110

DOI: 10.1016/j.insmatheco.2021.11.004

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