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An Inclusive Criterion For An Optimal Choice Of Reinsurance

Author

Listed:
  • EL ATTAR ABDERRAHIM

    (Department of Mathematics, Faculty of Sciences-Rabat, Mohamed V University, Morocco)

  • EL HACHLOUFI MOSTAFA

    (Department of Statistics and Mathematics, Applied to Economics and Management, Faculty of Juridical Sciences, Economic and Social-Ain Sebaa, Morocco)

  • GUENNOUN ZINE EL ABIDINE

    (Department of Mathematics, Faculty of Sciences-Rabat, Mohamed V University, Morocco)

Abstract

In this paper, we propose an inclusive model which allows to improve the results obtained in the literature with regard to the criteria set by the insurers such as, maximizing the expected technical benefit under the variance constraint (mean-variance), minimizing the probability of ruin and minimizing risk measures. In this model, we determine the optimal reinsurance treaty parameter that minimizes both the risk and the probability of ruin (by maximizing the Lundberg adjustment coefficient) under the constraint of the technical benefit which must also be maximal, based on the conditional tail variance (CTV) risk measure. Thus, we have developed an optimization procedure based on the augmented Lagrangian and genetic algorithms, in order to solve the optimization program of this model.

Suggested Citation

  • El Attar Abderrahim & El Hachloufi Mostafa & Guennoun Zine El Abidine, 2017. "An Inclusive Criterion For An Optimal Choice Of Reinsurance," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 1-22, December.
    • Handle: RePEc:wsi:afexxx:v:12:y:2017:i:04:n:s201049521750018x
    DOI: 10.1142/S201049521750018X
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    References listed on IDEAS

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    1. Ben Dbabis, Makram, 2012. "Modèles et méthodes actuarielles pour l'évaluation quantitative des risques en environnement solvabilité II," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/11415 edited by Hess, Christian.
    2. Kaluszka, Marek, 2001. "Optimal reinsurance under mean-variance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 61-67, February.
    3. Philippe Artzner, 1999. "Application of Coherent Risk Measures to Capital Requirements in Insurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 3(2), pages 11-25.
    4. Dickson, David C. M. & Waters, Howard R., 1996. "Reinsurance and ruin," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 61-80, December.
    5. Hald, Morten & Schmidli, Hanspeter, 2004. "On the Maximisation of the Adjustment Coefficient under Proportional Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 75-83, May.
    6. 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.
    7. Gajek, Leslaw & Zagrodny, Dariusz, 2000. "Insurer's optimal reinsurance strategies," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 105-112, August.
    8. Cai, Jun & Tan, Ken Seng, 2007. "Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 93-112, May.
    9. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    10. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
    11. Chi, Yichun & Tan, Ken Seng, 2011. "Optimal Reinsurance under VaR and CVaR Risk Measures: a Simplified Approach," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 487-509, November.
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