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Optimal Risk Transfer: A Numerical Optimization Approach

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  • Alexandru V. Asimit
  • Tao Gao
  • Junlei Hu
  • Eun-Seok Kim

Abstract

Capital efficiency and asset/liability management are part of the Enterprise Risk Management Process of any insurance/reinsurance conglomerate and serve as quantitative methods to fulfill the strategic planning within an insurance organization. A considerable amount of work has been done in this ample research field, but invariably one of the last questions is whether or not, numerically, the method is practically implementable, which is our main interest. The numerical issues are dependent on the traits of the optimization problem, and therefore we plan to focus on the optimal reinsurance design, which has been a very dynamic topic in the last decade. The existing literature is focused on finding closed-form solutions that are usually possible when economic, solvency, and other constraints are not included in the model. Including these constraints, the optimal contract can be found only numerically. The efficiency of these methods is extremely good for some well-behaved convex problems, such as Second-Order Conic Problems. Specific numerical solutions are provided to better explain the advantages of appropriate numerical optimization methods chosen to solve various risk transfer problems. The stability issues are also investigated together with a case study performed for an insurance group that aims capital efficiency across the entire organization.

Suggested Citation

  • Alexandru V. Asimit & Tao Gao & Junlei Hu & Eun-Seok Kim, 2018. "Optimal Risk Transfer: A Numerical Optimization Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(3), pages 341-364, July.
    • Handle: RePEc:taf:uaajxx:v:22:y:2018:i:3:p:341-364
    DOI: 10.1080/10920277.2017.1421472
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    Cited by:

    1. Fan, Qi & Tan, Ken Seng & Zhang, Jinggong, 2023. "Empirical tail risk management with model-based annealing random search," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 106-124.
    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. 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.

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