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Poisson processes and application to insurance and reliability theory

Presentation

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, reliability theory and population dynamics. Part of these Lectures will be dedicated to the statistical estimation of parameters in these models and to numerical analysis issues. The schedule of the Lectures is given as follows :

  •  Renewal and Poisson processes
  • Application to non-life insurance : risk process, ruin probabilities (Cramér-Lundberg model, asymptotic behavior).
  • Parameter estimation and numerical simulation for Poisson processes
  • Applications to reliability and population dynamics (continuous-time Markov chains, branching and  birth-death processes, queueing models)

Objectives

At the end of this module, the student will have understood and be able to explain (main concepts):

 

The main probabilistic models used for the risk analysis in different fields of application such as : insurance, reliability theory and population dynamics.

 

The student will be able to:

 

Develop a probabilistic model in which one can perform or numerically approximate :

  • The ruin probability associated to a non-life insurance contract
  • The probability of failure of a given device (reliability theory)
  • Characteristics of queuing systems and Some quantities arising in population dynamics

Needed prerequisite

  • Markov chains and applications (MIC 3)
  • Statistics (I3MIMT41)
  • Statistical modelling (I4MMMS71)
  • Advanced probabilities (GMM 4)

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...