A unified approach to the monotone integral-based premium principles under the CPT theory

Abstract

© 2020 Elsevier B.V. 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.