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Empirical Approach for Optimal Reinsurance Design

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  • Ken Seng Tan
  • Chengguo Weng

Abstract

This article proposes a novel and practical approach of addressing optimal reinsurance via an empirical approach. This method formulates reinsurance models using the observed data directly and has advantages including (1) transformation of an infinite dimensional optimization problem to a finite dimension, (2) no required explicit distributional assumption on the underlying risk, and (3) many empirical-based reinsurance models can be solved efficiently using the second-order conic programming. This allows insurers to incorporate many desirable objective functions and constraints while still retaining the ease of obtaining optimal reinsurance strategies. Numerical examples, including applications to actual Danish fire loss data, are provided to highlight the efficiency and the practicality of the proposed empirical models. The stability and consistency of the empirical-based solutions are also analyzed numerically.

Suggested Citation

  • Ken Seng Tan & Chengguo Weng, 2014. "Empirical Approach for Optimal Reinsurance Design," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(2), pages 315-342, April.
    • Handle: RePEc:taf:uaajxx:v:18:y:2014:i:2:p:315-342
    DOI: 10.1080/10920277.2014.888008
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    Citations

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    Cited by:

    1. 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.
    2. Guerra, M. & de Moura, A.B., 2021. "Reinsurance of multiple risks with generic dependence structures," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 547-571.
    3. Asimit, Alexandru V. & Cheung, Ka Chun & Chong, Wing Fung & Hu, Junlei, 2020. "Pareto-optimal insurance contracts with premium budget and minimum charge constraints," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 17-27.
    4. Kong, Dezhou & Liu, Lishan & Wu, Yonghong, 2018. "Optimal reinsurance under risk and uncertainty on Orlicz hearts," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 108-116.
    5. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel & Heras, Antonio, 2015. "Optimal reinsurance under risk and uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 61-74.
    6. Asimit, Alexandru V. & Hu, Junlei & Xie, Yuantao, 2019. "Optimal robust insurance with a finite uncertainty set," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 67-81.
    7. Yichun Chi & Zuo Quan Xu & Sheng Chao Zhuang, 2022. "Distributionally Robust Goal-Reaching Optimization in the Presence of Background Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 26(3), pages 351-382, August.
    8. Martin Eling & Ruo Jia, 2017. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2014 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 20(1), pages 63-77, March.
    9. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel & Heras, Antonio, 2022. "Risk transference constraints in optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 27-40.
    10. Asimit, Alexandru V. & Chi, Yichun & Hu, Junlei, 2015. "Optimal non-life reinsurance under Solvency II Regime," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 227-237.

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