Optimal Reinsurance Under CTV Risk Measure

  • Abderrahim El Attar
  • Mostafa El Hachloufi
  • Zine El Abidine Guennoun
Conference paper
Part of the Lecture Notes in Networks and Systems book series (LNNS, volume 37)


In this paper we proposed a new model for optimizing reinsurance which acts on the Conditional Tail Expectation (CTV) and the technical benefit. In this model, we have determined optimal reinsurance treaty parameters that minimize (CTV) under the constraint of technical benefit which must also be maximal. The minimization procedure is based on augmented Lagrangian method and genetic algorithms in order to solve the optimization program of this model.


Augmented Lagrangian Conditional Tail Variance Genetic algorithms Optimization Premium principle Reinsurance Technical benefit 


  1. 1.
    Andreani, R., Birgin, E.G., Martínez, J.M., Schuverdt, M.L.: On augmented Lagrangian methods with general lower-level constraint. SIAM J. Optim. 18, 1286–1302 (2007)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Artzner, P.: Application of coherent risk measures to capital requirements in insurance. North Am. Actuarial J. 3(2), 11–25 (1999)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Balbas, A., et al.: Optimal reinsurance with general risk measures. Insur. Math. Econ. 44, 374–384 (2009)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Dbabis, B.: Modèles et méthodes actuarielles pour l’évaluation quantitative des risques en environnement Solvabilité II. Thèse de doctorat, Université Paris Dauphine (2013)Google Scholar
  5. 5.
    Cai, J., Tan, K.S.: Optimal Retention for a stop loss reinsurance under the VaR and CTE risk measures. ASTIN Bull. 37, 93–112 (2007)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Denault, M.: Coherent allocation of risk capital. J. Risk 4, 1–34 (2001)CrossRefGoogle Scholar
  7. 7.
    Valdez, E.: On tail conditional variance and tail covariances. Faculty of Commerce and Economics, University of New South Wales Sydney, Australia (2004)Google Scholar
  8. 8.
    Tan, K.S., Weng, C., Zhang, Y.: Optimality of general reinsurance contracts under CTE risk measure. Insur. Math. Econ. 49(2), 175–187 (2011)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Kaas, R., et al.: Modern Actuarial Risk Theory. Kluwer Academic Publishers, Dordrecht (2001)MATHGoogle Scholar
  10. 10.
    Hong, L., Elshahat, A.: Conditionnal tail variance and conditionnal tail skewness in finance and insurance. Bradley University (2011)Google Scholar
  11. 11.
    Boudreault, M.: Mathématiques du risque, Document de référence, Département de mathématiques, Université du Québec à Montréal (2010)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Abderrahim El Attar
    • 1
  • Mostafa El Hachloufi
    • 2
  • Zine El Abidine Guennoun
    • 1
  1. 1.Department of Mathematics, Faculty of Sciences-RabatMohamed V UniversityRabatMorocco
  2. 2.Department of Statistics and MathematicsFaculty of Juridical Sciences, Economic and Social-Ain SebaaCasablancaMorocco

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