Abstract We consider the relationship between different types of the monotone integral-based premium principles. As a common frame for the CPT premium principle and the mean premium principle, the CPT-like integral-based premium principle is introduced and characterized. The Jensen-type inequalities for the Choquet integral and the CPT-like premium principle on the class of non-negative risks are proven. We establish conditions under which the Jensen-Steffensen-type inequalities for the CPT premium principle and the CPT-like premium principle hold for risks with finite range.

中文翻译：

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CPT理论下基于单调积分的保费原则的统一方法

摘要 我们考虑了不同类型的基于单调积分的保费原则之间的关系。作为CPT溢价原则和平均溢价原则的共同框架，引入并表征了类CPT积分式溢价原则。Choquet 积分的 Jensen 型不等式和非负风险类别的类 CPT 溢价原则得到证明。我们建立了 CPT 溢价原则和类 CPT 溢价原则的 Jensen-Steffensen 型不等式对有限范围风险成立的条件。