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Tail asymptotic expansions for L-statistics

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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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Authors and Affiliations

  1. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Lausanne, 1015, Switzerland

    Enkelejd Hashorva & ChengXiu Ling

  2. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    ZuoXiang Peng

Authors
  1. Enkelejd Hashorva
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  2. ChengXiu Ling
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  3. ZuoXiang Peng
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Correspondence to ZuoXiang Peng.

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Hashorva, E., Ling, C. & Peng, Z. Tail asymptotic expansions for L-statistics. Sci. China Math. 57, 1993–2012 (2014). https://doi.org/10.1007/s11425-014-4841-z

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  • DOI: https://doi.org/10.1007/s11425-014-4841-z

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