**DISCUSSION PAPER PI-0607**

**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).