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Optimal retention for a stop-loss reinsurance with incomplete information

Author

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  • Hu, Xiang
  • Yang, Hailiang
  • Zhang, Lianzeng

Abstract

This paper considers the determination of optimal retention in a stop-loss reinsurance. Assume that we only have incomplete information on a risk X for an insurer, we use an upper bound for the value at risk (VaR) of the total loss of an insurer after stop-loss reinsurance arrangement as a risk measure. The adopted method is a distribution-free approximation which allows to construct the extremal random variables with respect to the stochastic dominance order and the stop-loss order. We derive the optimal retention such that the risk measure used in this paper attains the minimum. We establish the sufficient and necessary conditions for the existence of the nontrivial optimal stop-loss reinsurance. For illustration purpose, some numerical examples are included and compared with the results yielded in Theorem 2.1 of Cai and Tan (2007).

Suggested Citation

  • Hu, Xiang & Yang, Hailiang & Zhang, Lianzeng, 2015. "Optimal retention for a stop-loss reinsurance with incomplete information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 15-21.
  • Handle: RePEc:eee:insuma:v:65:y:2015:i:c:p:15-21
    DOI: 10.1016/j.insmatheco.2015.08.005
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    References listed on IDEAS

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    1. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    2. Gerber, Hans U. & Smith, Nathaniel, 2008. "Optimal dividends with incomplete information in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 227-233, October.
    3. Cai, Jun & Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2008. "Optimal reinsurance under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 185-196, August.
    4. Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2011. "Optimality of general reinsurance contracts under CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 175-187, September.
    5. Cai, Jun & Tan, Ken Seng, 2007. "Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(01), pages 93-112, May.
    6. Wong, Man Hong & Zhang, Shuzhong, 2013. "Computing best bounds for nonlinear risk measures with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 204-212.
    7. Schepper, Ann De & Heijnen, Bart, 2007. "Distribution-free option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 179-199, March.
    8. Denuit, Michel & Vermandele, Catherine, 1998. "Optimal reinsurance and stop-loss order," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 229-233, July.
    9. Chi, Yichun & Tan, Ken Seng, 2011. "Optimal Reinsurance under VaR and CVaR Risk Measures: a Simplified Approach," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 41(02), pages 487-509, November.
    10. Carole Bernard & Weidong Tian, 2009. "Optimal Reinsurance Arrangements Under Tail Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 709-725.
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    Cited by:

    1. repec:eee:insuma:v:76:y:2017:i:c:p:48-55 is not listed on IDEAS
    2. 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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