We derive higher-order expansions of L-statistics of independent risks X_1,...,X_n under conditions on the underlying distribution function F.The new results are applied to derive the asymptotic expansions of ratios of two kinds of risk measures,stop-loss premium and excess return on capital,respectively.Several examples and a Monte Carlo simulation study show the efficiency of our novel asymptotic expansions.
In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.
