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Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle
Article

How Does Reinsurance Create Value to an Insurer? A Cost-Benefit Analysis Incorporating Default Risk

Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242-1409, USA
Academic Editor: Qihe Tang
Risks 2016, 4(4), 48; https://doi.org/10.3390/risks4040048
Received: 9 October 2016 / Revised: 5 December 2016 / Accepted: 7 December 2016 / Published: 16 December 2016
Reinsurance is often empirically hailed as a value-adding risk management strategy which an insurer can utilize to achieve various business objectives. In the context of a distortion-risk-measure-based three-party model incorporating a policyholder, insurer and reinsurer, this article formulates explicitly the optimal insurance–reinsurance strategies from the perspective of the insurer. Our analytic solutions are complemented by intuitive but scientifically rigorous explanations on the marginal cost and benefit considerations underlying the optimal insurance–reinsurance decisions. These cost-benefit discussions not only cast light on the economic motivations for an insurer to engage in insurance with the policyholder and in reinsurance with the reinsurer, but also mathematically formalize the value created by reinsurance with respect to stabilizing the loss portfolio and enlarging the underwriting capacity of an insurer. Our model also allows for the reinsurer’s failure to deliver on its promised indemnity when the regulatory capital of the reinsurer is depleted by the reinsured loss. The reduction in the benefits of reinsurance to the insurer as a result of the reinsurer’s default is quantified, and its influence on the optimal insurance–reinsurance policies analyzed. View Full-Text
Keywords: marginal cost; marginal benefit; distortion; 1-Lipschitz; premium; Value-at-Risk; VaR; TVaR; comonotonicity; counterparty risk marginal cost; marginal benefit; distortion; 1-Lipschitz; premium; Value-at-Risk; VaR; TVaR; comonotonicity; counterparty risk
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MDPI and ACS Style

Lo, A. How Does Reinsurance Create Value to an Insurer? A Cost-Benefit Analysis Incorporating Default Risk. Risks 2016, 4, 48. https://doi.org/10.3390/risks4040048

AMA Style

Lo A. How Does Reinsurance Create Value to an Insurer? A Cost-Benefit Analysis Incorporating Default Risk. Risks. 2016; 4(4):48. https://doi.org/10.3390/risks4040048

Chicago/Turabian Style

Lo, Ambrose. 2016. "How Does Reinsurance Create Value to an Insurer? A Cost-Benefit Analysis Incorporating Default Risk" Risks 4, no. 4: 48. https://doi.org/10.3390/risks4040048

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