Main Article Content


The objective of this research is to find the optimal retention level for a proportional reinsurance treaty based on the results of the convex optimization developed in De Finetti’s model. The latter makes it possible to determine the level of retention that achieves the expected profit by the insurer, while minimizing claims volatility. The convex functions appear abundantly in economics and finance. They have remarkable specificities that allows actuaries to minimize financial risks to which some institutions are exposed, especially insurance companies. Therefore, the use of mathematical tools to manage the various risks is paramount.In order to remedy the optimization problem, we have combined the probability of failure method with the "De Finetti" model for proportional reinsurance, which proposed a retention optimization process that minimizes claim volatility for a fixed expected profit based on the results of the non-linear optimization.

JEL Codes: C02, C25, C61, G22.


Convex function Nonlinear optimization Proportional reinsurance Risk minimization CAARAMA insurance campany

Article Details

Author Biographies

Zahra Cheraitia, National Higher School of Statistics and Applied Economics, Tipaza (Algeria)

PhD Student

Hanya Kherchi Medjden, National Higher School of Statistics and Applied Economics, Tipaza (Algeria)

Full Professor

How to Cite
Cheraitia, Z., & Kherchi Medjden, H. (2020). Application of Convex Optimization Results of De Finetti’s problem for Proportional Reinsurance (Study case CAARAMA insurance campany in Algiers). Management & Economics Research Journal, 2(4), 86-100.
Cited by


  1. Azcue, P. &Muler, N. (2005). Optimal reinsurance and dividend distribution policies in the Cramér–Lundberg model. Mathematical Finance. 15, 261-308.
  2. Blondeau, J & Partrat, C. (2003). La réassurance: approche technique [Reinsurance: atechnicalapproach]. Paris: Economica.
  3. Charpentier, A. (2010). La modélisation en réassurance [Reinsurance modeling]. Risques, 80, 36-41.
  4. Constantin, P. N, & Persson, L. E. (2006). Convex Functions and Their Applications. New York: Springer.
  5. Deelstra, G. & Plantin, G. (2006). Théorie du risque et réassurance [Risk theory and reinsurance]. Paris: Economica.
  6. Glineur, F. & Walhin, J. (2006). De Finetti’s retention problem for proportional reinsurance revisited. Blätter der DGVFM, 27, 451–462.
  7. Guarnieri, F. (2008). Le cadre juridique de la gestion des risques [The legal framework for risk management]. Paris: Tec and Doc.
  8. Hess, C. (2000). Methode actuarielles de l’assurance vie [Actuarial methods of life insurance]. Paris: Economica.
  9. Hull, J. (2013). Gestion des risques et institutions financière [Risk management and financial institutions] (3rd ed.). France : Pearson.
  10. Tosetti, A., Béhar, T., Fromenteau, M., & Ménart, S. (2011). Assurance : comptabilité, Réglementation, Actuariat [Insurance: accounting, Regulation, Actuarial] (2nd ed.). Paris: Economica.