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ST345 Life Contingencies

Lecturer(s): Professor Vassili Kolokoltsov

Restrictions: A previous restriction where students were not permitted to take this module as an unusual option has been removed. Students are now permitted to take this module if they have permission from all relevant parties via an Unusual Option form. Data Science students should note that they are not likely to be granted permission by the course director.

Prerequisite(s)/corequisite(s): ST218 Mathematical Statistics A, ST219 Mathematical Statistics B, ST334 Actuarial Methods, ST338 Actuarial Models

Commitment: 4 lectures per week, including example class. This module runs in Term 2.


  • Simple assurance and annuities, and their evaluation.
  • Net premiums and reserves.
  • Variable benefits and annuities.
  • Gross premiums and reserves for fixed and variable benefit contracts.
  • Annuities and assurances involving two lives.
  • Multiple state models, including multiple decrements.
  • Cashflow projection techniques.
  • Factors affecting mortality; selection and standardisation.

Aims: To cover the syllabus required for the Institute and Faculty of Actuaries (IFOA) exam "CT5 Contingencies", concerning financial schemes like pensions and life insurance where payments are contingent on the occurence or non-occurence of events such as death.

Objectives: At the end of the module, students should be able to

  • Define the actuarial symbols related to assurance and annuity contracts, understand their interrelationships, and perform relevant calculations.
  • Understand and use lifetables for calculations such as expected values and variances for simple contracts.
  • Describe and calculate net and gross premiums and premium reserves for various assurance and annuity contracts.
  • Describe and use methods to estimate cashflows for contracts involving two lives or multiple states, including the use of multiple decrement models.
  • Describe and use methods for assessing profitability and for pricing contracts.
  • Explain heterogeneity in populations, and simple methods to deal with heterogeneity.

To meet the syllabus requirements given by the IFOA for CT5, considerable additional work will be set in class, which won’t be covered in class, but may nonetheless be examinable.


  • Core Reading for the 2018 exams - CT5 Contingencies. Institute and Faculty of Actuaries (2018) [Available for purchase from the Undergraduate Support Office].;
  • Formulae and Tables for Examinations of the Faculty of Actuaries and the Institute of Actuaries. Institute of Actuaries and Faculty of Actuaries (2002) [Available on loan from the Undergraduate Support Office].;
  • Dickson, D.C., Hardy, M., Hardy, M.R. and Waters, H.R.. Actuarial mathematics for life contingent risks. Cambridge University Press, Second edition (2013).;
  • Dickson, D.C., Hardy, M., Hardy, M.R. and Waters, H.R.. Solutions manual for actuarial mathematics for life contingent risks. Cambridge University Press, Second edition (2013).; Turnbull, C.. A History of British Actuarial Thought. Palgrave Macmillan (2017).

Assessment: Two-hour examination (70%) and two one-hour class tests (15% each).

Deadlines: Class Test 1: Week 5, Class Test 2: Week 10.

Feedback: Feedback on class test 1 will be returned after two weeks. Feedback on class test 2 will be returned after three weeks.

Examination Period: Summer