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Poisson processes and application to insurance and reliability theory


The aim of these Lectures is to present the main probabilistic models at the basis of Risk analysis in several fields of application such as : insurance and reliability theory.

The Poisson process is widely used to model random "points" in time and space (e.g. claim arrivals in insurance, or failure times in reliability theory).

Furthermore, this model is widely used to construct number of other, more complicated, random processes (e.g. compound processes to model the risk in actuarial science).

The aim of this lecture is to introduce such models and study their fundamental properties from both probalistic and statistical aspects, with applications in reliability theroy and actuarial science.


This lecture is divided into two parts :


Part I : Big picture


Introduction of the theoretical tools for :

  • Homogeneous Poisson processes with application to reliability theory
  • Statistics for homogeneous Poisson rocesses
  • Compound Poisson processes with application to actuarial science
  • Inhomogeneous Poisson processes


Part II : Mini-Projects

Application and illustration on simulated data of different aspects of Poisson processes.


At the end of this module, the student should be able to :

  • Know and understand the Poisson process theory fundamentals
  • Estimate the rate of a homogeneous Poisson process and construct confidence intervals and statistical tests for such rate (theoretically and in practice with the R statistical Softwares).
  • State the main outlines of the compound Poisson process and Ruin theory
  • Apply and analyse the previous probabilistic theories to reliability therory and actuarial science.


Needed prerequisite

Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...