8. Continuous Payments

  1. S. David Promislow

Published Online: 13 JAN 2011

DOI: 10.1002/9781119971528.ch8

Fundamentals of Actuarial Mathematics, Second Edition

Fundamentals of Actuarial Mathematics, Second Edition

How to Cite

Promislow, S. D. (2010) Continuous Payments, in Fundamentals of Actuarial Mathematics, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119971528.ch8

Author Information

  1. York University, Toronto, Canada

Publication History

  1. Published Online: 13 JAN 2011
  2. Published Print: 17 DEC 2010

ISBN Information

Print ISBN: 9780470684115

Online ISBN: 9781119971528



  • continuous payments - annuities, payments made continuously;
  • insurance contracts, purchased by continuous premium payments - mathematical relationships;
  • continuous cases - not specifying actual payment at any point of time;
  • force of discount - continuous streams of cashflow evaluation, a new function;
  • constant interest case, and continuous annuities - analogous to discrete annuities;
  • continuous life annuities;
  • force of mortality - new quantity, analogous to force of discount;
  • insurances, at moment of death - continuous version, realistic model for insurance policies;
  • premiums and reserves - realistic model for life insurance, death benefits paid at moment of death, premiums periodically;
  • standard actuarial notation and terminology - benefits at moment of death, premiums continuous


This chapter contains sections titled:

  • Introduction to continuous annuities

  • The force of discount

  • The constant interest case

  • Continuous life annuities

  • The force of mortality

  • Insurances payable at the moment of death

  • Premiums and reserves

  • The general insurance–annuity identity in the continuous case

  • Differential equations for reserves

  • Some examples of exact calculation

  • Standard actuarial notation and terminology

  • Notes and references

  • Exercises