Tail-preserving Distortion Risk Measure For Three Parameter Distributions

To provide incentive for active risk management, it is argued that a sound coherent distortion risk measure should preserve some higher degree stop-loss orders, at least the degree three convex order. Such risk measures are called tail-preserving risk measures. It is shown that under some conditions, the Wang right-tail measure are preserved under the degree three convex order for three-parameter distributions, Burr and Weibull distributions.