ST301      Half Unit
Actuarial Mathematics (Life)

This information is for the 2022/23 session.

Teacher responsible

Dr Andreas Sojmark


This course is compulsory on the BSc in Actuarial Science. This course is available on the BSc in Business Mathematics and Statistics, BSc in Data Science and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.


Students must have completed:

EITHER Probability, Distribution Theory and Inference (ST202) OR Probability and Distribution Theory (ST206)

AND Survival Models (ST227).

Course content

Single life mortality models, assurance and annuity contracts and their actuarial notation, computation of their present values and variances; relations among the present values of the various contracts.

The equivalence principle: computation of net premiums for the main assurance policies.

Prospective and retrospective reserves, Thiele's differential equation as the main tool for the computation of reserves.

Expenses: gross premium and gross reserves. Selection effect and how it affects mortality tables.

Multi-life assurance contracts: joint life and last survival life, computation of premiums and reserves for the main two-lives contracts.

Multi-states mortality models: basic notions of continuous-time Markov chains, Kolmogorov backward and forward equations, application to multiple decrements and disability models, computation of transition intensities.

Thiele differential equation for multi-states models, computation and analysis of reserves for main multi-state policies.

With-profit policies, unit-linked assurance policies, pensions.

Interplay between assurance and finance: embedded options, market consistent actuarial valuation.


This course will be delivered through a combination of seminars, lectures and Q&A sessions totalling a minimum of 30 hours across in the Michaelmas Term.

Formative coursework

Compulsory written answers to one set of problems.

Indicative reading

R Norberg, Basic Life Insurance Mathematics; The Institute of Actuaries, Core reading Subject CT5

Dickson, Hardy, Waters, 'Actuarial Mathematics for Life Contingent Risks'

Wutrich, Buhlmann, Furrer, 'Market Consistent Actuarial Valuation'


Exam (90%, duration: 3 hours) in the January exam period.
Coursework (10%) in the period between MT and LT.

The project will be timed (2hr + submission time)

Student performance results

(2019/20 - 2021/22 combined)

Classification % of students
First 59.3
2:1 18.7
2:2 12.4
Third 7.2
Fail 2.4

Key facts

Department: Statistics

Total students 2021/22: 75

Average class size 2021/22: 26

Capped 2021/22: No

Value: Half Unit

Guidelines for interpreting course guide information

Course selection videos

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Personal development skills

  • Problem solving
  • Application of information skills
  • Application of numeracy skills
  • Commercial awareness
  • Specialist skills