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On optimal reinsurance policy with distortion risk measures and premiums

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  • Assa, Hirbod

Abstract

In this paper, we consider the problem of optimal reinsurance design, when the risk is measured by a distortion risk measure and the premium is given by a distortion risk premium. First, we show how the optimal reinsurance design for the ceding company, the reinsurance company and the social planner can be formulated in the same way. Second, by introducing the “marginal indemnification functions”, we characterize the optimal reinsurance contracts. We show that, for an optimal policy, the associated marginal indemnification function only takes the values zero and one. We will see how the roles of the market preferences and premiums and that of the total risk are separated.

Suggested Citation

  • Assa, Hirbod, 2015. "On optimal reinsurance policy with distortion risk measures and premiums," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 70-75.
  • Handle: RePEc:eee:insuma:v:61:y:2015:i:c:p:70-75
    DOI: 10.1016/j.insmatheco.2014.11.007
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. repec:eee:apmaco:v:313:y:2017:i:c:p:103-118 is not listed on IDEAS
    2. Wenjun Jiang & Jiandong Ren & Ričardas Zitikis, 2017. "Optimal Reinsurance Policies under the VaR Risk Measure When the Interests of Both the Cedent and the Reinsurer Are Taken into Account," Risks, MDPI, Open Access Journal, vol. 5(1), pages 1-22, February.
    3. Hirbod Assa, 2015. "Optimal risk allocation in a market with non-convex preferences," Papers 1503.04460, arXiv.org.
    4. Amir T. Payandeh Najafabadi & Ali Panahi Bazaz, 2017. "An Optimal Multi-layer Reinsurance Policy under Conditional Tail Expectation," Papers 1701.05447, arXiv.org.
    5. repec:bpj:strimo:v:35:y:2018:i:1-2:p:35-50:n:3 is not listed on IDEAS
    6. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2016. "The role of a representative reinsurer in optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 196-204.
    7. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.
    8. Tim J. Boonen, 2016. "Optimal Reinsurance with Heterogeneous Reference Probabilities," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-11, July.
    9. Mi Chen & Wenyuan Wang & Ruixing Ming, 2016. "Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-12, December.

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