Testing hypotheses about the equality of several risk measure values with applications in insurance

This paper explores statistical tests about the equality of risk measure values obtained using a distortion-based risk measure. We consider both the case in which the risk measure value is specified in the null hypothesis and the case in which it is not. In the former case, one- and two-sided alternatives are considered, and in the latter case, ordered and unordered alternatives are considered. Asymptotically most powerful tests are obtained, and asymptotic distributions of the test statistics are found using results about the asymptotic distributions of the risk measure values. Finally, we consider a numerical example and conclude the paper with notes on when the results of the paper could, or could not, be safely used.