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Optimal reinsurance with general premium principles

Yichun Chi () and Ken Seng Tan

Insurance: Mathematics and Economics, 2013, vol. 52, issue 2, 180-189

Abstract: In this paper, we study two classes of optimal reinsurance models from the perspective of an insurer by minimizing its total risk exposure under the criteria of value at risk (VaR) and conditional value at risk (CVaR), assuming that the reinsurance premium principles satisfy three basic axioms: distribution invariance, risk loading and stop-loss ordering preserving. The proposed class of premium principles is quite general in the sense that it encompasses eight of the eleven commonly used premium principles listed in Young (2004). Under the additional assumption that both the insurer and reinsurer are obligated to pay more for larger loss, we show that layer reinsurance is quite robust in the sense that it is always optimal over our assumed risk measures and the prescribed premium principles. We further use the Wang’s and Dutch premium principles to illustrate the applicability of our results by deriving explicitly the optimal parameters of the layer reinsurance. These two premium principles are chosen since in addition to satisfying the above three axioms, they exhibit increasing relative risk loading, a desirable property that is consistent with the market convention on reinsurance pricing.

Keywords: Conditional value at risk; Value at risk; Layer reinsurance; Wang’s premium principle; Dutch premium principle (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.insmatheco.2012.12.001

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