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

Bounds for Distorted Risk Measures

“…For concave distortion functions one can compute upper bounds for D g (Ψ) whenever Ψ is the sum of the risks or a function like stop-loss sum using stochastic ordering properties (see [7]). If there are only two risk factors, it is also possible to obtain lower bounds.…”

“…If it is possible to compute the bounds following the approach proposed by Goncalves et al [7], which, in fact, has the advantages to provide sharp bounds and require only simple computations, then the following method should be applied in cases where stochastic ordering relations are no longer useful (for instance, in the case of convex distortion function).…”