ENSAE Paris - École d'ingénieurs pour l'économie, la data science, la finance et l'actuariat

Risk Theory - 3A/MS/M2


ROBERT Christian-Yann

Department: Finance


The purpose of this course is to present the basic mathematical concepts of damage insurance. The objective of Risk Theory is to provide theoretical models of the cost and number of claims in order to deduce the associated risk and to price insurance contracts.
At the end of this course, students should be able to : 

  • Use the individual and collective model of claims occurrence in non-life insurance.
  • Apply the collective model to insurance
  • Understanding the Poisson process and its application in ruin theory


  1. Preliminaries - Reminders, generating functions. 
  2. Insurance models - Individual model, collective model.
  3. Risk comparison.
  4. Premium principle and risk measurement.
  5. Theory of ruin - Poisson's process, Lundberg's model, probability of ruin.



  • Beard R., Pentikainen R., & E. Pesonen (1984), Risk Theory. Chapman and Hall [INSEE].
  • Buhlmann H.  (1970), Mathematical Methods in Risk Theory. Springer [36 BUH 00 A].
  • Charpentier, A., & M. Denuit (2004), Mathématiques de l'assurance Non-Vie, tome 1: Principes Fondamentaux de la Théorie du Risque. Economica [36 DEN 00 B].
  • Daikin, C.D., Pentikainen, T., & M. Pesonen (1994), Practical Risk Theory for Actuaries. Chapmann and Hall [78 DAY 00 A].
  • Gerber, H.(1979), An Introduction to Mathematical Risk Theory. Huebner Foundation for insurance [78 GER 00 A].
  • Heilmann, W. R. (1988), Fundamentals of Risk Theory, VVW Karlsruhe [36 HEI 00 A].
  • Straub, E. (1988), Non Life Insurance Mathematics. Springer [78 STR 00 A].