Tail asymptotic expansions for L-statistics |
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| Authors: | Enkelejd Hashorva ChengXiu Ling ZuoXiang Peng |
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| Institution: | 1. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Lausanne, 1015, Switzerland
2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China
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| Abstract: | 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. |
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| Keywords: | smoothly varying condition second-order regular variation tail asymptotics value-at-risk conditional tail expectation largest claims reinsurance ratio of risk measure excess return on capital |
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