Optimal Layers for Catastrophe Reinsurance

By Luyang Fu, C.K. Stan Khury

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Insurers purchase catastrophe reinsurance primarily to reduce underwriting risk in any one experience period and thus enhance the stability of their income stream over time. Reinsurance comes at a cost and therefore it is important to maintain a balance between the perceived benefit of buying catastrophe reinsurance and its cost. This study presents a methodology for determining the optimal catastrophe reinsurance layer by maximizing the risk-adjusted underwriting profit within a classical mean-variance framework.
From the perspective of enterprise risk management, this paper improves the existing literature in two ways. First, it considers catastrophe and noncatastrophe losses simultaneously. Previous studies focused on catastrophe losses only. Second, risk is measured by lower partial moment which we believe is a more reasonable and flexible measure of risk compared to the traditional variance and Value at Risk (VaR) approaches.

KEYWORDS: Catastrophe reinsurance layer, downside risk, lower partial moment, semivariance, utility function, enterprise risk management

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Fu, Luyang, and C.K. Stan Khury, "Optimal Layers for Catastrophe Reinsurance," Variance 4:2, 2010, pp. 191-208.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.