20. Poisson Processes

  1. S. David Promislow

Published Online: 14 JAN 2011

DOI: 10.1002/9781119971528.ch20

Fundamentals of Actuarial Mathematics, Second Edition

Fundamentals of Actuarial Mathematics, Second Edition

How to Cite

Promislow, S. D. (2010) Poisson Processes, in Fundamentals of Actuarial Mathematics, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119971528.ch20

Author Information

  1. York University, Toronto, Canada

Publication History

  1. Published Online: 14 JAN 2011
  2. Published Print: 17 DEC 2010

ISBN Information

Print ISBN: 9780470684115

Online ISBN: 9781119971528



  • Poisson processes, continuous-time process - index set T, taking all values in interval;
  • process, with independent increments - over disjoint time intervals, being independent;
  • counting process, a stochastic process N(t) - counting number of ‘events’;
  • Poisson process - in modeling a counting situation;
  • properties of Poisson process - features of Poisson processes, interesting applications;
  • Poisson process and distribution of arrival times;
  • nonhomogeneous Poisson processes - stationarity assumption, rate of occurrence varying with time;
  • compound Poisson process - corresponding to compound Poisson distribution;
  • compound Poisson surplus process;
  • model for surplus process


This chapter contains sections titled:

  • Introduction

  • Definition of a Poisson process

  • Waiting times

  • Some properties of a Poisson process

  • Nonhomogeneous Poisson processes

  • Compound Poisson processes

  • Notes and references

  • Exercises