A note on Choquet integrals and imprecise market premium functionals

Wood, Jacob;Jang, Lee-Chae

Abstract

The concept of imprecise market premiums as a measure of insurance risk is motivated by the goal to represent these imprecise premiums through the use of extended interval numbers. In order [to] achieve this we consider interval-valued Choquet integrals that contain both imprecise distorted probabilities and decumulative distribution functions. In this paper, we present four axioms to describe the bahavior of insurance prices in an imprecise competitive market setting. For these axioms, we prove the interval-valued Choquet integral representation with respect to an imprecise distorted probability and investigate some characterizations of imprecise market premiums.

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Proceedings of Jangjeon Mathematical Society

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1598-7564

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Jangjeon Mathematical Society

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Daegu, South Korea

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