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Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account

Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Qihe Tang
Risks 2017, 5(1), 11; https://doi.org/10.3390/risks5010011
Received: 18 November 2016 / Revised: 4 January 2017 / Accepted: 17 January 2017 / Published: 5 February 2017
Optimal forms of reinsurance policies have been studied for a long time in the actuarial literature. Most existing results are from the insurer’s point of view, aiming at maximizing the expected utility or minimizing the risk of the insurer. However, as pointed out by Borch (1969), it is understandable that a reinsurance arrangement that might be very attractive to one party (e.g., the insurer) can be quite unacceptable to the other party (e.g., the reinsurer). In this paper, we follow this point of view and study forms of Pareto-optimal reinsurance policies whereby one party’s risk, measured by its value-at-risk (VaR), cannot be reduced without increasing the VaR of the counter-party in the reinsurance transaction. We show that the Pareto-optimal policies can be determined by minimizing linear combinations of the VaR s of the two parties in the reinsurance transaction. Consequently, we succeed in deriving user-friendly, closed-form, optimal reinsurance policies and their parameter values. View Full-Text
Keywords: optimal reinsurance treaties; value at risk; Pareto optimality optimal reinsurance treaties; value at risk; Pareto optimality
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MDPI and ACS Style

Jiang, W.; Ren, J.; Zitikis, R. Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account. Risks 2017, 5, 11. https://doi.org/10.3390/risks5010011

AMA Style

Jiang W, Ren J, Zitikis R. Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account. Risks. 2017; 5(1):11. https://doi.org/10.3390/risks5010011

Chicago/Turabian Style

Jiang, Wenjun, Jiandong Ren, and Ričardas Zitikis. 2017. "Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account" Risks 5, no. 1: 11. https://doi.org/10.3390/risks5010011

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