Tail asymptotic expansions for L-statistics

Enkelejd Hashorva; Cheng Xiu Ling; Zuo Xiang Peng

doi:10.1007/s11425-014-4841-z

Tail asymptotic expansions for L-statistics

Enkelejd Hashorva, Cheng Xiu Ling, Zuo Xiang Peng

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We derive higher-order expansions of L-statistics of independent risks X₁, ...,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.

Original language	English
Pages (from-to)	1993-2012
Number of pages	20
Journal	Science China Mathematics
Volume	57
Issue number	10
DOIs	https://doi.org/10.1007/s11425-014-4841-z
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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10.1007/s11425-014-4841-z

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title = "Tail asymptotic expansions for L-statistics",

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.",

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",

author = "Enkelejd Hashorva and Ling, {Cheng Xiu} and Peng, {Zuo Xiang}",

note = "Funding Information: Acknowledgements This work was supported by the Swiss National Science Foundation (Grant Nos. 200021-1401633/1, 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), National Natural Science Foundation of China (Grant No. 11171275) and the Natural Science Foundation Project of Chongqing (Grant No. cstc2012jjA00029). The authors are grateful to the anonymous referees for their careful reading and helpful suggestions which greatly improved the paper.",

year = "2014",

month = oct,

doi = "10.1007/s11425-014-4841-z",

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T1 - Tail asymptotic expansions for L-statistics

AU - Hashorva, Enkelejd

AU - Ling, Cheng Xiu

AU - Peng, Zuo Xiang

N1 - Funding Information: Acknowledgements This work was supported by the Swiss National Science Foundation (Grant Nos. 200021-1401633/1, 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), National Natural Science Foundation of China (Grant No. 11171275) and the Natural Science Foundation Project of Chongqing (Grant No. cstc2012jjA00029). The authors are grateful to the anonymous referees for their careful reading and helpful suggestions which greatly improved the paper.

PY - 2014/10

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N2 - 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.

AB - 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.

KW - conditional tail expectation

KW - excess return on capital

KW - largest claims reinsurance

KW - ratio of risk measure

KW - second-order regular variation

KW - smoothly varying condition

KW - tail asymptotics

KW - value-at-risk

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DO - 10.1007/s11425-014-4841-z

M3 - Article

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VL - 57

SP - 1993

EP - 2012

JO - Science China Mathematics

JF - Science China Mathematics

IS - 10

ER -

Tail asymptotic expansions for L-statistics

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Keywords

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