Pricing insurance premia: a top down approach

  • Eymen ErraisEmail author
S.I.: Risk Management Decisions and Value under Uncertainty


Insurance plays an important economic and social role through its ability to transfer risk. In this paper, we focus on the largest insurance sector, the automobile sector. We model automobile insurance premia through a top down approach. Our approach is appealing since it defines the dynamics of the aggregate loss in a consistent way, and also provides a coherent definition of the joint distribution of the total losses and the car insurance premium. We show how to make this top down approach computationally tractable by using the class of affine point processes, which are intensity-based jump processes driven by affine jump diffusions. An affine point process is sufficiently flexible to account for both country global infrastructure and driving behaviour. Further it allows for efficient computation and calibration of a large class of insurance products.


Insurance Car accidents Stochastic modeling Self exciting processes 

JEL Classification

G12 G13 



  1. Benlagha, N., & Karaa, I. (2017). Evidence of adverse selection in automobile insurance market : A seemingly unrelated probit modelling. Cogent Economics and Finance, 5, 133–149.CrossRefGoogle Scholar
  2. Benlagha, N., Charfeddine, L., & Karaa, I. (2012). Modeling accident occurence in car insurance implementation on tunisian data. Asian-African Journal of Economics and Econometrics, 12(2), 395–406.Google Scholar
  3. Brigo, D., Pallavicini, A., & Torresetti, R. (2006). Calibration of cdo tranches with the dynamical generalized-poisson loss model. Working paper, Banca IMI.Google Scholar
  4. Duffie, D., Pan, J., & Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68, 1343–1376.CrossRefGoogle Scholar
  5. Duffie, D., Filipovic, D., & Schachermayer, W. (2003). Affine processes and applications in finance. Annals of Applied Probability, 13, 984–1053.CrossRefGoogle Scholar
  6. Errais, E., Giesecke, K., & Goldberg, L. (2010). Affine point processes and portfolio credit risk. SIAM Journal on Financial Mathematics, 1, 642–665.CrossRefGoogle Scholar
  7. Giesecke, K., & Goldberg, L. (2005). A top down approach to multi-name credit. Working paper, Stanford University.Google Scholar
  8. Giesecke, K., & Schwenkler, G. (2018). Filtered likelihood for point processes. Journal of Econometrics, 204, 33–53.CrossRefGoogle Scholar
  9. Giesecke, K., & Tomecek, P. (2005). Dependent events and changes of time. Working paper, Cornell University.Google Scholar
  10. Giesecke, K, Shkolnik, A., Teng, G., & Wei, Y. (2019). Numerical solution of jump-diffusion sdes. Operations research, forthcoming.Google Scholar
  11. Hawkes, A. G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58(1), 83–90.CrossRefGoogle Scholar
  12. Hawkes, A. G., & Oakes, D. (1974). A cluster process representation of a self-exciting process. Journal of Applied Probability, 11, 493–503.CrossRefGoogle Scholar
  13. Karaa, I., & Benlagha, N. (2015). Testing for asymmetric information in tunisian automobile insurance market. Mediterranean Journal of Social Sciences, 6(3), 455–465.Google Scholar
  14. Kwiecinski, A., & Szekli, R. (1996). Some monotonicty and dependent properties of self-exciting point processes. The Annals of Applied Probability, 6(4), 1211–1231.CrossRefGoogle Scholar
  15. Revuz, D., & Yor, M. (2005). Continuous martingales and Brownian motion. Heidelberg: Springer.Google Scholar
  16. Schönbucher, P. (2005). Portflio losses and the term structure of loss transition rates: A new methodology for pricing of portfolio of credit derivatives. Working paper, Department of mathematics, ETH Zurich.Google Scholar
  17. Sidenius, J., Piterbarg, V., & Andersen, L. (2005). A new framework for dynamic credit portfolio loss modelling. Working paper.Google Scholar
  18. Wang, J., Liu, B., Ting, F., Liu, S., & Stpancic, J. (2018). Modeling when and where a secondary accident occurs. Accident Analysis and Prevention, 1, 450–458.Google Scholar
  19. Zhang, X., Blanchet, J., Giesecke, K., & Glynn, P. (2015). Affine point processes : Approximation and efficient simulation. Mathematics of Operations Research, 40, 797–819.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratoire de Recherche en Economie Quantitative du Développement (LAREQUAD)University of Tunis, Tunis Business SchoolTunisTunisia

Personalised recommendations