• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.489-503
• /
• 2007

In this paper, we define signed interval-valued Choquet integrals which have numerous applications in mathematical economics, informatiom theory, expected utility theory, and risk analysis on interval-valued random variables, for examples: interval-valued random payments and interval-valued random profiles, etc. And we discuss axiomatic characterizations of them. Furthermore, we fine some condition that comonotonic additivity of symmetric Choquet integrals on interval-valued random payments is satisfied and give two examples related the main theorem.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.121-131
• /
• 2009

In this paper we examine the relation among law-invariant coherent risk measures with the Fatou property, distortion risk measures and spectral risk measures, and give a new proof of the relation among them. It is also shown that the spectral risk measure satisfies the monotonicity with respect to stochastic dominance and the comonotonic additivity.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2007.04a
• /
• pp.209-212
• /
• 2007

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 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.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.4
• /
• pp.451-454
• /
• 2007

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.