TY - JOUR
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
Y1 - 2014/10
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
UR - http://www.scopus.com/inward/record.url?scp=84906092708&partnerID=8YFLogxK
U2 - 10.1007/s11425-014-4841-z
DO - 10.1007/s11425-014-4841-z
M3 - Article
AN - SCOPUS:84906092708
SN - 1674-7283
VL - 57
SP - 1993
EP - 2012
JO - Science China Mathematics
JF - Science China Mathematics
IS - 10
ER -