We derive higher-order expansions of L-statistics of independent risks X1,..., Xn under conditions on the underlying distribution function F. The new results are applied to derive the asymptotic expansions of ratios o...We derive higher-order expansions of L-statistics of independent risks X1,..., Xn 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. Keywords smoothly varying condition, second-order regular variation, tail asymptotics, value-at-risk, con- ditional tail expectation, largest claims reinsurance, ratio of risk measure, excess return on capital展开更多
基金supported by the Swiss National Science Foundation(Grant Nos.2000211401633/1,200021-134785 and 200021-1401633/1)Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme(Grant No.RARE-318984)+1 种基金National Natural Science Foundation of China(Grant No.11171275)the Natural Science Foundation Project of Chongqing(Grant No.cstc2012jjA00029)
文摘We derive higher-order expansions of L-statistics of independent risks X1,..., Xn 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. Keywords smoothly varying condition, second-order regular variation, tail asymptotics, value-at-risk, con- ditional tail expectation, largest claims reinsurance, ratio of risk measure, excess return on capital
