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

Author

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  • Mi Chen

    (School of Mathematics and Computer Science & FJKLMAA, Fujian Normal University, Fuzhou 350108, China)

  • Wenyuan Wang

    (School of Mathematical Sciences, Xiamen University, Xiamen 361005, Fujian, China
    School of Applied Mathematics, Xinjiang University of Finance and Economics, Urumchi 830012, Xinjiang, China)

  • Ruixing Ming

    (School of Statistics and Mathematics, ZheJiang GongShang University, Hangzhou 310018, China)

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 * .

Suggested Citation

  • Mi Chen & Wenyuan Wang & Ruixing Ming, 2016. "Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle," Risks, MDPI, vol. 4(4), pages 1-12, December.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:4:p:50-:d:85321
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    References listed on IDEAS

    as
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