Testing for the order of risk measures: an application of L-statistics in actuarial science

摘要

In this paper, we present and discuss non-parametric and parametric approaches for testing the order of two risk measures. The approaches are based on obtaining asymptotic results for the difference between two empirical risk measures. In the non-parametric case, our investigations rely heavily on the "alternative" representation of risk measures emphasized and utilized by Jones and Zitikis (2003). In the parametric case, our investigations are in line with those of Brazauskas and Kaiser (2004). Simple and easily verifiable assumptions are used throughout the paper, thus making the results readily applicable in practice. A simulation study illustrates the results.