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Risks 2016, 4(4), 50; doi:10.3390/risks4040050

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

1
School of Mathematics and Computer Science & FJKLMAA, Fujian Normal University, Fuzhou 350108, China
2
School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, China
3
School of Statistics and Mathematics, ZheJiang GongShang University, Hangzhou 310018, China
4
School of Applied Mathematics, Xinjiang University of Finance and Economics, Urumchi 830012, Xinjiang, China
*
Author to whom correspondence should be addressed.
Academic Editor: Qihe Tang
Received: 13 June 2016 / Revised: 2 December 2016 / Accepted: 9 December 2016 / Published: 16 December 2016
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Abstract

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 * . View Full-Text
Keywords: reinsurance; general law-invariant risk measure; TVaR premium principle reinsurance; general law-invariant risk measure; TVaR premium principle
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Chen, M.; Wang, W.; Ming, R. Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle. Risks 2016, 4, 50.

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