On PBIL, DE and PSO for Optimization of Reinsurance Contracts

  • Omar Andres Carmona CortesEmail author
  • Andrew Rau-Chaplin
  • Duane Wilson
  • Jürgen Gaiser-Porter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8602)


In this paper, we study from the perspective of an insurance company the Reinsurance Contract Placement problem. Given a reinsurance contract consisting of a fixed number of layers and a set of expected loss distributions (one per layer) as produced by a Catastrophe Model, plus a model of current costs in the global reinsurance market, identifying optimal combinations of placements (percent shares of sub-contracts) such that for a given expected return the associated risk value is minimized. Our approach explores the use bio-inpired metaheuristics with the goal of determining which evolutionary optimization approach leads to the best results for this problem, while being executable in a reasonable amount of time on realistic industrial sized problems.


Reinsurance Analytics Reinsurance Contract Placement Particle Swarm Optimization Differential Evolution Population-Based Incremental Learning Financial Risk Optimization 


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  1. 1.
    Cai, J., et al.: Optimal reinsurance under VaR and CTE risk measures. Insurance: Mathematics and Economics 43, 185–196 (2008)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Grossi, P., Kunreuther, H.: Catastrophe Modeling: A New Approach to Managing Risk. International Series on Risk, Insurance and Economic Scurity. Springer (2005)Google Scholar
  3. 3.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995)Google Scholar
  4. 4.
    Storn, R., Price, K.: Differential Evolution A simple and efficient adaptive scheme for global optimization over continuous spaces, Technical Report TR-95-012 (March 1995).
  5. 5.
    Storn, R., Price, K.: Minimizing the real functions of the ICEC 1996 contest by differential evolution. In: Proc. of IEEE International Conference on Evolutionary Computation, Nagoya, Japan (1996)Google Scholar
  6. 6.
    Michalewicz, Z.: Genetic Algorithms + Data Structure = Evolution Programs, 3rd edn Springer (1996)Google Scholar
  7. 7.
    Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Transactions on Evolutionary Computation 3(2), 82–102 (1999)CrossRefGoogle Scholar
  8. 8.
    Baluja, S.: Population based incremental learning. Technical Report, Carnegie Mellon UniversityGoogle Scholar
  9. 9.
    Edward Tsang, P.K., Martinez-Jaramillo, S.: Computational finance feature article. IEEE Computational Intelligence Society (2004)Google Scholar
  10. 10.
    Gilli, M., Schumann, E.: Heuristic optimisation in nancial modelling. COMISEF wps-007 (2009)Google Scholar
  11. 11.
    Maringer, D.G., Meyer, M.: CSmooth transition autoregressive models: New approaches to the model selection problem. Studies in Nonlinear Dynamics and Econometrics 12(1), 1–19 (2008)Google Scholar
  12. 12.
    Krink, T., Paterlini, S.: Multiobjective optimization using Differential Evolution for real-world portfolio optimization. Computational Management Science 8, 157–179 (2011)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Shapiro, A.F., Gorman, R.P.: Implementing adaptive nonlinear models. Insurance: Mathematics and Economics 26(2–3), 289–307 (2000)zbMATHGoogle Scholar
  14. 14.
    Salcedo-Sanz, S., Carro Calvo, L., Claramunt Bielsa, M., Castañer, A., Marmol, M.: An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approache (2013). Available at SSRN: or
  15. 15.
    Mistry, S. (n.d.), et al.: Parallel Computation of Reinsurance Models (unpublished manuscript)Google Scholar
  16. 16.
    Cortes, O.A.C., Rau-Chaplin, A., Wilson, D., Gaiser-Porterz, J.: Efficient Optimization of Reinsurance Contracts using Discretized PBIL. In: Proceedings of Data Analytics, London (2013)Google Scholar
  17. 17.
    Posík, P., Huyer, W., Pál, L.: A comparison of global search algorithms for continuous black box optimization. Evolutionary Computation 20, 509–541 (2012)Google Scholar
  18. 18.
    Sebag, M., Ducoulombier, A.: Extending Population-Based Incremental Learning to Continuous Search Spaces. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 418–427. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  19. 19.
    Bureerat, S.: Improved Population-Based Incremental Learning in Continuous Spaces. In: Gaspar-Cunha, A., Takahashi, R., Schaefer, G., Costa, L. (eds.) Soft Computing in Industrial Applications. AISC, vol. 96, pp. 77–86. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  20. 20.
    Mitschele, A., Oesterreicher1, I., Schlottmann, F., Seese1, D.: Heuristic optimization of reinsurance programs and implications for reinsurance buyers. In: International Conference of the German Operations Research Society (2006)Google Scholar
  21. 21.
    Sun, C., Zhou, H., Chen, L.: Improved differential evolution algorithms. In: IEEE International Conference on Computer Science and Automation Engineering, vol. 3, pp. 142–145 (2012)Google Scholar
  22. 22.
    Yuan, B., Gallagher, M.: Playing in continuous spaces: Some analysis and extension of population-based incremental learning. In: CEC 2003, CA, USA, pp. 443–450 (2003)Google Scholar
  23. 23.
    Servais, M.P., Jager, G., Greene, J.R.: Function optimisation using multi-base population based incremental learning. In: PRASA 1997. Rhodes University (1997)Google Scholar
  24. 24.
    Pehlivanoglu, Y.V.: A New Particle Swarm Optimization Method Enhanced With a Periodic Mutation Strategy and Neural Networks. IEEE Transactions on Evolutionary Computation 17(3), 436–452 (2013)Google Scholar
  25. 25.
    Schefler, B.: Statistics: Concepts and Applications. Benjamin-Cummings Pub. Co. (1988)Google Scholar
  26. 26.
    Clerc, M.: A method to improve Standard PSO, Open access archive HAL (2009). Available at (last Visit June 6, 2013)

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Omar Andres Carmona Cortes
    • 1
    Email author
  • Andrew Rau-Chaplin
    • 2
  • Duane Wilson
    • 2
  • Jürgen Gaiser-Porter
    • 3
  1. 1.Instituto Federal do MaranhãoSão LuisBrasil
  2. 2.Risk Analytics LabDalhousie UniversityHalifaxCanada
  3. 3.Global Analytics, Willis GroupLondonUK

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