Abstract
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.
Original language | English |
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Pages (from-to) | 1993-2012 |
Number of pages | 20 |
Journal | Science China Mathematics |
Volume | 57 |
Issue number | 10 |
DOIs | |
Publication status | Published - Oct 2014 |
Externally published | Yes |
Keywords
- conditional tail expectation
- excess return on capital
- largest claims reinsurance
- ratio of risk measure
- second-order regular variation
- smoothly varying condition
- tail asymptotics
- value-at-risk
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Hashorva, E., Ling, C. X., & Peng, Z. X. (2014). Tail asymptotic expansions for L-statistics. Science China Mathematics, 57(10), 1993-2012. https://doi.org/10.1007/s11425-014-4841-z