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Risk-Minimizing Reinsurance Protection For Multivariate Risks

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  • K. C. Cheung
  • K. C. J. Sung
  • S. C. P. Yam

Abstract

type="main" xml:lang="en"> In this article, we study the problem of optimal reinsurance policy for multivariate risks whose quantitative analysis in the realm of general law-invariant convex risk measures, to the best of our knowledge, is still absent in the literature. In reality, it is often difficult to determine the actual dependence structure of these risks. Instead of assuming any particular dependence structure, we propose the minimax optimal reinsurance decision formulation in which the worst case scenario is first identified, then we proceed to establish that the stop-loss reinsurances are optimal in the sense that they minimize a general law-invariant convex risk measure of the total retained risk. By using minimax theorem, explicit form of and sufficient condition for ordering the optimal deductibles are also obtained.

Suggested Citation

  • K. C. Cheung & K. C. J. Sung & S. C. P. Yam, 2014. "Risk-Minimizing Reinsurance Protection For Multivariate Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(1), pages 219-236, March.
  • Handle: RePEc:bla:jrinsu:v:81:y:2014:i:1:p:219-236
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    Cited by:

    1. Nicole Bauerle & Alexander Glauner, 2017. "Optimal Risk Allocation in Reinsurance Networks," Papers 1711.10210, arXiv.org.
    2. Zhu, Yunzhou & Chi, Yichun & Weng, Chengguo, 2014. "Multivariate reinsurance designs for minimizing an insurer’s capital requirement," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 144-155.
    3. Sun, Haoze & Weng, Chengguo & Zhang, Yi, 2017. "Optimal multivariate quota-share reinsurance: A nonparametric mean-CVaR framework," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 197-214.

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