17. The Collective Risk Model

  1. S. David Promislow

Published Online: 14 JAN 2011

DOI: 10.1002/9781119971528.ch17

Fundamentals of Actuarial Mathematics, Second Edition

Fundamentals of Actuarial Mathematics, Second Edition

How to Cite

Promislow, S. D. (2010) The Collective Risk Model, in Fundamentals of Actuarial Mathematics, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119971528.ch17

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



  • risk theory, the collective risk model - and individual risk model;
  • estimating total amount paid on group of policies - collective risk model;
  • dynamic multi-period version - of collective risk model;
  • collective risk model, for casualty insurance - as automobile, home or health policies;
  • collision, claimed under automobile policy - amount for a dented fender;
  • collective risk model, and total claims - as compound distribution;
  • mean and variance of S;
  • generating functions, same conditioning techniques - deducing moment generating function;
  • choosing a frequency distribution;
  • recursion formula for S-X taking positive integers as values - recursion formula for computing probability function of S


This chapter contains sections titled:

  • Introduction

  • The mean and variance of S

  • Generating functions

  • Exact distribution of S

  • Choosing a frequency distribution

  • Choosing a severity distribution

  • Handling the point mass at 0

  • Counting claims of a particular type

  • The sum of two compound Poisson distributions

  • Deductibles and other modifications

  • A recursion formula for S

  • Notes and references

  • Exercises