Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Interval-valued Choquet integrals and applications in pricing risks

구간치 쇼케이적분과 위험률 가격 측정에서의 응용

  • Jang, Lee-Chae (Dept. of Mathematics and Computer Science, Konkuk University)
  • 장이채 (건국대학교 컴퓨터응용과학부 전산수학)
  • Published : 2007.08.25
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Abstract

Non-additive measures and their corresponding Choquet integrals are very useful tools which are used in both insurance and financial markets. In both markets, it is important to update prices to account for additional information. The update price is represented by the Choquet integral with respect to the conditioned non-additive measure. In this paper, we consider a price functional H on interval-valued risks defined by interval-valued Choquet integral with respect to a non-additive measure. In particular, we prove that if an interval-valued pricing functional H satisfies the properties of monotonicity, comonotonic additivity, and continuity, then there exists an two non-additive measures ${\mu}1,\;{\mu}2$ such that it is represented by interval-valued choquet integral on interval-valued risks.

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