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Enhancing Insurer Value Using Reinsurance and Value-at-Risk Criterion

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  • Ken Seng Tan

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada.
    China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, China.)

  • Chengguo Weng

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada.)

Abstract

The quest for optimal reinsurance design has remained an interesting problem among insurers, reinsurers, and academicians. An appropriate use of reinsurance could reduce the underwriting risk of an insurer and thereby enhance its value. This paper complements the existing research on optimal reinsurance by proposing another model for the determination of the optimal reinsurance design. The problem is formulated as a constrained optimization problem with the objective of minimizing the value-at-risk of the net risk of the insurer while subjecting to a profitability constraint. The proposed optimal reinsurance model, therefore, has the advantage of exploiting the classical tradeoff between risk and reward. Under the additional assumptions that the reinsurance premium is determined by the expectation premium principle and the ceded loss function is confined to a class of increasing and convex functions, explicit solutions are derived. Depending on the risk measure's level of confidence, the safety loading for the reinsurance premium, and the expected profit guaranteed for the insurer, we establish conditions for the existence of reinsurance. When it is optimal to cede the insurer's risk, the optimal reinsurance design could be in the form of pure stop-loss reinsurance, quota-share reinsurance, or a combination of stop-loss and quota-share reinsurance.

Suggested Citation

  • Ken Seng Tan & Chengguo Weng, 2012. "Enhancing Insurer Value Using Reinsurance and Value-at-Risk Criterion," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(1), pages 109-140, March.
    • Handle: RePEc:pal:genrir:v:37:y:2012:i:1:p:109-140
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    Citations

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    Cited by:

    1. Najafabadi, Amir T. Payandeh & Bazaz, Ali Panahi, 2018. "An optimal multi-layer reinsurance policy under conditional tail expectation," Annals of Actuarial Science, Cambridge University Press, vol. 12(1), pages 130-146, March.
    2. Chi, Yichun & Tan, Ken Seng & Zhuang, Sheng Chao, 2020. "A Bowley solution with limited ceded risk for a monopolistic reinsurer," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 188-201.
    3. Olufemi Adebowale Abass, 2019. "Empirical Analysis of Reinsurance Dependence on the Profitability of General Insurance Business in Nigeria," Academic Journal of Economic Studies, Faculty of Finance, Banking and Accountancy Bucharest,"Dimitrie Cantemir" Christian University Bucharest, vol. 5(4), pages 36-43, December.
    4. Nanjun ZHU & Yulin FENG, 2017. "Optimal Change-Loss Reinsurance Contract Design under Tail Risk Measures for Catastrophe Insurance," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(4), pages 225-242.
    5. Chi, Yichun & Liu, Fangda, 2021. "Enhancing an insurer's expected value by reinsurance and external financing," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 466-484.
    6. Chi, Yichun & Weng, Chengguo, 2013. "Optimal reinsurance subject to Vajda condition," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 179-189.
    7. Jean-François Outreville, 2014. "The Meaning of Risk? Insights from The Geneva Risk and Insurance Review," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 39(4), pages 768-781, October.
    8. 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.

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