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

Risk Theory


ROBERT Christian-Yann

Department: Finance


The aim of this course is to present the basic mathematical concepts used in general insurance. The Theory of Risk aims to provide theoretical models of cost and accident frequency in order to deduce the insurer's probability of ruin and to value insurance contracts


  1. Premium calculation principle and risk comparison- The pure premium. Premium calculation principles. Risk comparison. Modelling the heterogeneity of the portfolio.
  2. Individual and collective risk models- The compound Poisson model. Individual/collective risk models.
  3. Risk theory and probability of ruin- The Poisson process. The Lundberg model. The 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].