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Stable solutions for optimal reinsurance problems involving risk measures

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  • Balbás, Alejandro
  • Balbás, Beatriz
  • Heras, Antonio

Abstract

The optimal reinsurance problem is a classic topic in actuarial mathematics. Recent approaches consider a coherent or expectation bounded risk measure and minimize the global risk of the ceding company under adequate constraints. However, there is no consensus about the risk measure that the insurer must use, since every risk measure presents advantages and shortcomings when compared with others. This paper deals with a discrete probability space and analyzes the stability of the optimal reinsurance with respect to the risk measure that the insurer uses. We will demonstrate that there is a "stable optimal retention" that will show no sensitivity, insofar as it will solve the optimal reinsurance problem for many risk measures, thus providing a very robust reinsurance plan. This stable optimal retention is a stop-loss contract, and it is easy to compute in practice. A fast linear time algorithm will be given and a numerical example presented.

Suggested Citation

  • Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," European Journal of Operational Research, Elsevier, vol. 214(3), pages 796-804, November.
  • Handle: RePEc:eee:ejores:v:214:y:2011:i:3:p:796-804
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    2. repec:eee:ejores:v:262:y:2017:i:2:p:720-732 is not listed on IDEAS
    3. repec:eee:ejores:v:267:y:2018:i:2:p:778-790 is not listed on IDEAS
    4. Mitra, Sovan & Date, Paresh & Mamon, Rogemar & Wang, I-Chieh, 2013. "Pricing and risk management of interest rate swaps," European Journal of Operational Research, Elsevier, vol. 228(1), pages 102-111.
    5. Heras, Antonio & Balbas Aparicio, Raquel & Balbas Aparicio, Beatriz & Balbas de la Corte, Alejandro, 2014. "Optimal reinsurance under risk and uncertainty," INDEM - Working Paper Business Economic Series id-14-04, Instituto para el Desarrollo Empresarial (INDEM).
    6. 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.
    7. repec:eee:ejores:v:266:y:2018:i:3:p:1175-1188 is not listed on IDEAS

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