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Risk Measures and Comonotonicity: a Review

J. Dhaene S. Vanduffel Q. Tang M. J. Goovaerts R. Kaas D. Vyncke

In this paper we examine and summarize properties of several well-known
risk measures that can be used in the framework of setting solvency capital
requirements for a risky business. Special attention is given to the class of
(concave) distortion risk measures. We investigate the relationship between
these risk measures and theories of choice under risk. Furthermore we consider
the problem of how to evaluate risk measures for sums of non-independent
random variables. Approximations for such sums, based on the concept of
comonotonicity, are proposed. Several examples are provided to illustrate
properties or to prove that certain properties do not hold. Although the paper
contains several new results, it is written as an overview and pedagogical
introduction to the subject of risk measurement. The paper is an extended
version of Dhaene et al. (2003).