Tail asymptotics of generalized deflated risks with insurance applications

Chengxiu Ling; Zuoxiang Peng

doi:10.1016/j.insmatheco.2016.09.012

Tail asymptotics of generalized deflated risks with insurance applications

Chengxiu Ling^*
, Zuoxiang Peng

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

Let X and S∈(0,1) be two independent risk variables. This paper investigates approximations of generalized deflated risks E{X^κI{SX>;x}} with a flexible constant κ≥0 under extreme value theory framework. Our findings are illustrated by three applications concerning higher-order tail approximations of deflated risks as well as approximations of the Haezendonck–Goovaerts and expectile risk measures. Numerical analyses show that higher-order approximations obtained in this paper significantly improve lower-order approximations.

Original language	English
Pages (from-to)	220-231
Number of pages	12
Journal	Insurance: Mathematics and Economics
Volume	71
DOIs	https://doi.org/10.1016/j.insmatheco.2016.09.012
Publication status	Published - 1 Nov 2016
Externally published	Yes

Keywords

Deflated risks
Expectile
Extreme value theory
Haezendonck–Goovaerts risk measure
Second-order/third-order regular variations

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10.1016/j.insmatheco.2016.09.012

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title = "Tail asymptotics of generalized deflated risks with insurance applications",

abstract = "Let X and S∈(0,1) be two independent risk variables. This paper investigates approximations of generalized deflated risks E\{XκI\{SX>;x\}\} with a flexible constant κ≥0 under extreme value theory framework. Our findings are illustrated by three applications concerning higher-order tail approximations of deflated risks as well as approximations of the Haezendonck–Goovaerts and expectile risk measures. Numerical analyses show that higher-order approximations obtained in this paper significantly improve lower-order approximations.",

keywords = "Deflated risks, Expectile, Extreme value theory, Haezendonck–Goovaerts risk measure, Second-order/third-order regular variations",

author = "Chengxiu Ling and Zuoxiang Peng",

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year = "2016",

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doi = "10.1016/j.insmatheco.2016.09.012",

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T1 - Tail asymptotics of generalized deflated risks with insurance applications

AU - Ling, Chengxiu

AU - Peng, Zuoxiang

PY - 2016/11/1

Y1 - 2016/11/1

N2 - Let X and S∈(0,1) be two independent risk variables. This paper investigates approximations of generalized deflated risks E{XκI{SX>;x}} with a flexible constant κ≥0 under extreme value theory framework. Our findings are illustrated by three applications concerning higher-order tail approximations of deflated risks as well as approximations of the Haezendonck–Goovaerts and expectile risk measures. Numerical analyses show that higher-order approximations obtained in this paper significantly improve lower-order approximations.

AB - Let X and S∈(0,1) be two independent risk variables. This paper investigates approximations of generalized deflated risks E{XκI{SX>;x}} with a flexible constant κ≥0 under extreme value theory framework. Our findings are illustrated by three applications concerning higher-order tail approximations of deflated risks as well as approximations of the Haezendonck–Goovaerts and expectile risk measures. Numerical analyses show that higher-order approximations obtained in this paper significantly improve lower-order approximations.

KW - Deflated risks

KW - Expectile

KW - Extreme value theory

KW - Haezendonck–Goovaerts risk measure

KW - Second-order/third-order regular variations

UR - https://www.scopus.com/pages/publications/84994035328

U2 - 10.1016/j.insmatheco.2016.09.012

DO - 10.1016/j.insmatheco.2016.09.012

M3 - Article

AN - SCOPUS:84994035328

SN - 0167-6687

VL - 71

SP - 220

EP - 231

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

ER -

Tail asymptotics of generalized deflated risks with insurance applications

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Keywords

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