Bounds for Quantile-Based Risk Measures of Functions of Dependent Random Variables

This paper introduces two techniques for computing bounds for several quantile-based risk measures based on distortion functions. Knowledge about the marginal distribution of the involved random variables is assumed with the optional assumption of some partial information about the structure of dependence. The aim is to derive bounds for risk measures of functions of dependent random variables. Several examples taken from an insurance context are given. We use Embrechts et al. (2003) methodology and the stochastic ordering approach to derive bounds for various risk measures in the bi-dimensional and the multidimensional cases.