Results 51 to 60 of about 90 (78)

A note on -expectation with comonotonic additivity

Statistics and Probability Letters, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Long Jiang
exaly   +3 more sources

On positive homogeneity and comonotonic additivity of the principle of equivalent utility under Cumulative Prospect Theory

Insurance: Mathematics and Economics, 2020
The paper deals with the principle of equivalent utility under cumulative prospect theory. After presenting the main definitions and some basic properties, the study focuses on certain characteristics of the premium. In particular, the analysis poses a critical point: the results concerning positive homogeneity and comonotonic additivity are in general
Jacek Chudziak
exaly   +3 more sources

A new characterization of distortion premiums via countable additivity for comonotonic risks

Insurance: Mathematics and Economics, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xianyi Wu, Xian Zhou
exaly   +3 more sources

Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals

Statistics and Risk Modeling, 2006
SUMMARY The purpose of our paper is to link some results on the Choquet integrals with the theory of coherent risk measures. Using this link we establish some properties of dilatation monotone and comonotonic coherent measures of risk.
Johannes Leitner
exaly   +3 more sources

Boundedness and symmetry of comonotonically additive functionals

Fuzzy Sets and Systems, 2001
A relationship between the Choquet integral and comonotically additive and monotone functionals \(I\) is reexamined. First, some necessary and sufficient conditions are given for the boundedness of \(I\) in terms of Narukawa's fuzzy measures. Then there is proved that \(I\) is symmetric if and only if it can be represented by the Šipoš integral.
Yasuo Narukawa, Toshiaki Murofushi, Michio Sugeno   +2 more
openaire   +2 more sources

Extension and representation of comonotonically additive functionals

Fuzzy Sets and Systems, 2001
Two real functions \(f\), \(g\) are comonotonic, if \(f(x_1)< f(x_2)\) implies \(g(x_1)\leq g(x_2)\) for any \(x_1\), \(x_2\). The set \(K\) of all functions with compact support in a locally compact Hausdorff space is considered. A real-valued functional \(I\) on \(K\) is called comonotonically additive if \(I(f+ g)= I(f)+ I(g)\) whenever \(f,g\in K\)
Yasuo Narukawa, Toshiaki Murofushi, Michio Sugeno   +2 more
openaire   +2 more sources

Comonotonic Random Sets and Its Additivity of Choquet Integrals

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2017
In this paper, we propose a concept of comonotonicity of random sets, which is a set inclusion relation and generalized notion of comonotonicity of real-valued random variables. Then we study some elementary properties of comonotonicity of random sets and comonotonic additivity of real-valued Choquet integral for random set mappings.
Gaofeng Zong, Zengjing Chen, Faisal Shahzad   +2 more
openaire   +1 more source

Regular fuzzy measure and representation of comonotonically additive functional

Fuzzy Sets and Systems, 2000
Two real-valued functions \(f,g: X\to\mathbb{R}\) are called comonotonic if \(f(x)< f(x')\) implies \(g(x)\leq g(x')\) for all \(x,x'\in X\). A functional \(I: K\to\mathbb{R}\) on a space of real-valued functions is called comonotonically additive if \(I(f+g)= I(f)+ I(g)\) for any pair of comonotonic functions of \(K\). It is proved that a functional \(
Yasuo Narukawa, Toshiaki Murofushi, Michio Sugeno   +2 more
openaire   +2 more sources

A representation of a comonotone--additive and monotone functional by two Sugeno integrals

Fuzzy Sets and Systems, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Endre Pap, Biljana P. Mihailovic
openaire   +1 more source

A symmetric conjugate condition for the representation of comonotonically additive and monotone functionals

Fuzzy Sets and Systems, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hashem Parvaneh Masiha, M. Rahmati
openaire   +1 more source