Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle

Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle

In this paper, we study the optimal reinsurance problem where risks of the insurer are measured by general law-invariant risk measures and premiums are calculated under the TVaR premium principle, which extends the work of the expected premium principle. Our objective is to characterize the optimal...

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Bibliographic Details
Main Authors: Mi Chen, Wenyuan Wang, Ruixing Ming
Format: Article
Language:English
Published: MDPI AG 2016-12-01
Series:Risks
Subjects:
reinsurance
general law-invariant risk measure
TVaR premium principle
Online Access:http://www.mdpi.com/2227-9091/4/4/50
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spelling doaj-fbd9aca06ffa44e9abf2f09efcc269a82020-11-25T00:04:26ZengMDPI AGRisks2227-90912016-12-01445010.3390/risks4040050risks4040050Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium PrincipleMi Chen0Wenyuan Wang1Ruixing Ming2School of Mathematics and Computer Science & FJKLMAA, Fujian Normal University, Fuzhou 350108, ChinaSchool of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, ChinaSchool of Statistics and Mathematics, ZheJiang GongShang University, Hangzhou 310018, ChinaIn this paper, we study the optimal reinsurance problem where risks of the insurer are measured by general law-invariant risk measures and premiums are calculated under the TVaR premium principle, which extends the work of the expected premium principle. Our objective is to characterize the optimal reinsurance strategy which minimizes the insurer’s risk measure of its total loss. Our calculations show that the optimal reinsurance strategy is of the multi-layer form, i.e., f * ( x ) = x ∧ c * + ( x - d * ) + with c * and d * being constants such that 0 ≤ c * ≤ d * .http://www.mdpi.com/2227-9091/4/4/50reinsurancegeneral law-invariant risk measureTVaR premium principle
collection DOAJ
language English
format Article
sources DOAJ
author Mi Chen
Wenyuan Wang
Ruixing Ming
spellingShingle Mi Chen
Wenyuan Wang
Ruixing Ming
Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle
Risks
reinsurance
general law-invariant risk measure
TVaR premium principle
author_facet Mi Chen
Wenyuan Wang
Ruixing Ming
author_sort Mi Chen
title Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle
title_short Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle
title_full Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle
title_fullStr Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle
title_full_unstemmed Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle
title_sort optimal reinsurance under general law-invariant convex risk measure and tvar premium principle
publisher MDPI AG
series Risks
issn 2227-9091
publishDate 2016-12-01
description In this paper, we study the optimal reinsurance problem where risks of the insurer are measured by general law-invariant risk measures and premiums are calculated under the TVaR premium principle, which extends the work of the expected premium principle. Our objective is to characterize the optimal reinsurance strategy which minimizes the insurer’s risk measure of its total loss. Our calculations show that the optimal reinsurance strategy is of the multi-layer form, i.e., f * ( x ) = x ∧ c * + ( x - d * ) + with c * and d * being constants such that 0 ≤ c * ≤ d * .
topic reinsurance
general law-invariant risk measure
TVaR premium principle
url http://www.mdpi.com/2227-9091/4/4/50
work_keys_str_mv AT michen optimalreinsuranceundergenerallawinvariantconvexriskmeasureandtvarpremiumprinciple
AT wenyuanwang optimalreinsuranceundergenerallawinvariantconvexriskmeasureandtvarpremiumprinciple
AT ruixingming optimalreinsuranceundergenerallawinvariantconvexriskmeasureandtvarpremiumprinciple
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