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Journals / Hacettepe Journal of Mathematics and Statistics / 2016 / Cilt: 45 - Sayı: 2

Optimal stop-loss reinsurance: a dependence analysis

Anna Castañer
M. Mercè Claramunt
Pages
497–519
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Secondly, the optimal stop-loss contract is obtained if the criterion used is the maximization of the joint survival probability of the insurer and the reinsurer in one period.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The stop-loss reinsurance is one of the most important reinsurance contracts in the insurance market.
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Key Findings & Data:From the insurer point of view, it presents an interesting property: it is optimal if the criterion of minimizing the variance of the cost of the insurer is used.
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Conclusion & Impact:Secondly, the optimal stop-loss contract is obtained if the criterion used is the maximization of the joint survival probability of the insurer and the reinsurer in one period.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Stop-loss premium · Survival probabilities · Reinsurance

Abstract

The stop-loss reinsurance is one of the most important reinsurance contracts in the insurance market. From the insurer point of view, it presents an interesting property: it is optimal if the criterion of minimizing the variance of the cost of the insurer is used. The aim of the paper is to contribute to the analysis of the stop-loss contract in one period from the point of view of the insurer and the reinsurer. Firstly, the influence of the parameters of the reinsurance contract on the correlation coefficient between the cost of the insurer and the cost of the reinsurer is studied. Secondly, the optimal stop-loss contract is obtained if the criterion used is the maximization of the joint survival probability of the insurer and the reinsurer in one period.

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Cite This Article

Castañer, A., Claramunt, M. M. (2022). Optimal stop-loss reinsurance: a dependence analysis. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 2, 497–519. https://ajindex.com/articles/530161

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References (14)

  1. Assa, H. On optimal reinsurance policy with distortion risk measures and premiums, Insur. Math. Econ. 61, 70-75, 2015.
  2. Azcue, P. and Muler, N. Optimal reinsurance and dividend distribution policies in the Cramér-Lundberg model, Math. Financ. 15 (2), 261-308, 2005. Balbás, A., Balbás, B., Balbás, R. and Heras, A. Optimal reinsurance under risk and incertainty, Insur. Math. Econ. 60, 61-74, 2015. Balbás, A., Balbás, R. and Heras, A. Optimal reinsurance with general risk measures, Insur. Math. Econ. 44 (3), 374-384, 2009.
  3. Bohman, H. and Esscher, F. Studies in risk theory with numerical illustrations concerning distribution functions and stop loss premiums. Part I, Scand. Actuar. J. 1963 (3-4), 173- 225, 1963.
  4. Borch, K. An attempt to determine the optimum amount of stop loss reinsurance, Transactions of the 16th International Congress of Actuaries I, 597-610, 1960.
  5. Borch, K. The optimal reinsurance treaty, Astin Bull. 5 (2), 293-297, 1969.
  6. Borch, K. The mathematical theory of insurance (Lexington Books, Lexington, 1974).
  7. Cai, J. and Tan, K. S. Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures, Astin Bull. 37 (1), 93-112, 2007.
  8. Cai, J., Fang, Y., Li, Z. and Willmot, G. E. Optimal reciprocal reinsurance treaties under the joint survival probability and the joint profitable probability, J. Risk Insur. 80 (1), 145-168, 2013.
  9. Cai, J., Tan, K. S., Weng, C. and Zhang, Y. Optimal reinsurance under VaR and CTE risk measures, Insur. Math. Econ. 43 (1), 185-196, 2008. Castañer, A., Claramunt, M. M. and Lefèvre, C. Survival probabilities in bivariate risk models, with application to reinsurance, Insur. Math. Econ. 53 (3), 632-642, 2013. Castañer, A., Claramunt, M. M. and Mármol, M. Ruin probability and time of ruin with a proportional reinsurance threshold strategy, Top 20 (3), 614-638, 2012.
  10. Centeno, M. L. and Simões, O. Optimal reinsurance, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 103 (2), 387-404, 2009.
  11. Cheung, K. C. Optimal reinsurance revisited - a geometric approach, Astin Bull. 40 (1), 221-239, 2010.
  12. Cui, W., Yang, J. and Wu, L. Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles, Insur. Math. Econ. 53 (1), 74-85, 2013
  13. Daykin, C. D., Pentikainen, T. and Pesonen, M. Practical risk theory for actuaries (Chapman and Hall, London, 1994).
  14. Denuit, M. and Charpentier, A. Mathématiques de l’assurance non-vie: Tome 1, Principes fondamentaux de théorie du risque (Economica, Paris,