Portfolio risk analysis of excess of loss reinsurance

Qihe Tang; Zhiwei Tong; Li Xun

doi:10.1016/j.insmatheco.2021.11.004

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Portfolio risk analysis of excess of loss reinsurance

Journal article

Peer reviewed

Portfolio risk analysis of excess of loss reinsurance

Qihe Tang, Zhiwei Tong and Li Xun

Insurance, mathematics & economics, Vol.102, pp.91-110

01/2022

DOI: 10.1016/j.insmatheco.2021.11.004

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Abstract

•Analyze a large XL reinsurance portfolio of losses modeled by a mixture structure.•Determine the limit of the infimal retention level under a VaR-based solvency capital requirement.•Establish a weak convergence of LLN-type for the reinsurance portfolio loss.•Derive approximations to the distortion risk measures of the reinsurance portfolio loss. 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.

Distortion risk measures

Law of large numbers

Mixture

Retention

Solvency capital requirement

Details

Title: Subtitle: Portfolio risk analysis of excess of loss reinsurance
Creators: Qihe Tang - UNSW Sydney
Zhiwei Tong - UNSW Sydney
Li Xun - Changchun University
Resource Type: Journal article
Publication Details: Insurance, mathematics & economics, Vol.102, pp.91-110
DOI: 10.1016/j.insmatheco.2021.11.004
ISSN: 0167-6687
eISSN: 1873-5959
Publisher: Elsevier B.V
Grant note: DOI: 10.13039/501100001809, name: National Natural Science Foundation of China, award: 11701043; DOI: 10.13039/100015539, name: Australian Government; DOI: 10.13039/501100000923, name: Australian Research Council, award: DP200101859; DOI: 10.13039/501100001773, name: University of New South Wales
Language: English
Date published: 01/2022
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9984257733502771

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