Nonparametric inference for sensitivity of Haezendonck–Goovaerts risk measure

Recently Haezendonck-Goovaerts (H-G) risk measure has been popular in actuarial science. When it is applied to an insurance or a financial portfolio with several loss variables, sensitivity analysis becomes useful in managing the portfolio, and the assumption of independent observations may not be reasonable. This paper first derives an expression for computing the sensitivity of the H-G risk measure, which enables us to estimate the sensitivity nonparametrically via the H-G risk measure. Further, we derive the asymptotic distributions of the nonparametric estimators for the H-G risk measure and the sensitivity by assuming that loss variables in the portfolio follow from a strictly stationary -mixing sequence. A simulation study is provided to examine the finite sample performance of the proposed nonparametric estimators. Finally, the method is applied to a real data set.