Second-order tail asymptotics of deflated risks

Enkelejd Hashorva; Chengxiu Ling; Zuoxiang Peng

doi:10.1016/j.insmatheco.2014.04.003

Second-order tail asymptotics of deflated risks

Enkelejd Hashorva, Chengxiu Ling^*, Zuoxiang Peng

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

Random deflation of risk models is an interesting topic for both theoretical and practical actuarial problems. In this paper, we investigate second-order tail asymptotics of the deflated risk X = R S under the assumptions of second-order regular variation on the survival functions of the risk R and the deflator S. Our findings are applied to derive second-order expansions of Value-at-Risk. Further we investigate the estimation of small tail probability for deflated risks and then discuss the asymptotics of the aggregated deflated risk.

Original language	English
Pages (from-to)	88-101
Number of pages	14
Journal	Insurance: Mathematics and Economics
Volume	56
Issue number	1
DOIs	https://doi.org/10.1016/j.insmatheco.2014.04.003
Publication status	Published - May 2014
Externally published	Yes

Keywords

Estimation of tail probability
Random deflation
Risk aggregation
Second-order regular variation
Value-at-Risk

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10.1016/j.insmatheco.2014.04.003

Cite this

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title = "Second-order tail asymptotics of deflated risks",

abstract = "Random deflation of risk models is an interesting topic for both theoretical and practical actuarial problems. In this paper, we investigate second-order tail asymptotics of the deflated risk X = R S under the assumptions of second-order regular variation on the survival functions of the risk R and the deflator S. Our findings are applied to derive second-order expansions of Value-at-Risk. Further we investigate the estimation of small tail probability for deflated risks and then discuss the asymptotics of the aggregated deflated risk.",

keywords = "Estimation of tail probability, Random deflation, Risk aggregation, Second-order regular variation, Value-at-Risk",

author = "Enkelejd Hashorva and Chengxiu Ling and Zuoxiang Peng",

note = "Funding Information: We are indebted to the referees for suggestions which improved the manuscript significantly. The authors acknowledge partial support by the Swiss National Science Foundation grants 200021-134785 , 200021-140633/1 and RARE -318984 (an FP7 Marie Curie IRSES Fellowship). The third author was also supported by the National Natural Science Foundation of China grant o.11171275 and the Natural Science Foundation Project of CQ no. cstc2012jjA00029. ",

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doi = "10.1016/j.insmatheco.2014.04.003",

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AU - Hashorva, Enkelejd

AU - Ling, Chengxiu

AU - Peng, Zuoxiang

N1 - Funding Information: We are indebted to the referees for suggestions which improved the manuscript significantly. The authors acknowledge partial support by the Swiss National Science Foundation grants 200021-134785 , 200021-140633/1 and RARE -318984 (an FP7 Marie Curie IRSES Fellowship). The third author was also supported by the National Natural Science Foundation of China grant o.11171275 and the Natural Science Foundation Project of CQ no. cstc2012jjA00029.

PY - 2014/5

Y1 - 2014/5

N2 - Random deflation of risk models is an interesting topic for both theoretical and practical actuarial problems. In this paper, we investigate second-order tail asymptotics of the deflated risk X = R S under the assumptions of second-order regular variation on the survival functions of the risk R and the deflator S. Our findings are applied to derive second-order expansions of Value-at-Risk. Further we investigate the estimation of small tail probability for deflated risks and then discuss the asymptotics of the aggregated deflated risk.

AB - Random deflation of risk models is an interesting topic for both theoretical and practical actuarial problems. In this paper, we investigate second-order tail asymptotics of the deflated risk X = R S under the assumptions of second-order regular variation on the survival functions of the risk R and the deflator S. Our findings are applied to derive second-order expansions of Value-at-Risk. Further we investigate the estimation of small tail probability for deflated risks and then discuss the asymptotics of the aggregated deflated risk.

KW - Estimation of tail probability

KW - Random deflation

KW - Risk aggregation

KW - Second-order regular variation

KW - Value-at-Risk

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DO - 10.1016/j.insmatheco.2014.04.003

M3 - Article

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VL - 56

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EP - 101

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

IS - 1

ER -

Second-order tail asymptotics of deflated risks

Abstract

Keywords

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