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Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals
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Pavel G. Grigoriev
Published/Copyright:
September 25, 2009
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. In particular it is shown that on an atomless probability space dilatation monotone and comonotonic additive coherent risk measures have to be law invariant.
Key words and phrases: capacity; dilatation monotonicity; comonotonicity; coherent risk measure; risk-adjusting value functional; Choquet integral; law invariant risk measure; comonotonic additivity
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Received: 2005-December-21
Accepted: 2006-March-03
Published Online: 2009-09-25
Published in Print: 2006-07
© R. Oldenbourg Verlag, München
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Articles in the same Issue
- Editorial preface
- Risk measurement with equivalent utility principles
- Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals
- On distortion functionals
- Convex risk measures and the dynamics of their penalty functions
- Law invariant convex risk measures for portfolio vectors
- Robust utility maximization in a stochastic factor model
- Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints
- On the optimal risk allocation problem
- Monetary utility over coherent risk ratios
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