F70LB Life Insurance Mathematics B

Dr Larry O’BrienIan Sharpe

Course co-ordinator(s): Dr Larry O’Brien (Malaysia), Ian Sharpe (Edinburgh).


This course aims:

  • to introduce some more advanced topics in life insurance mathematics, and complete the material covered in Subject CT5


  • Thiele’s differential equation
  • Markov multiple-state models
  • risk reserves
  • insurances written on multiple lives
  • the features of disability and long-term care insurance and pension contracts
  • heterogeneity and selection
  • single-figure indices
  • profit testing conventional insurance contracts
  • profit testing unit-linked contracts

Detailed Information

Course Description: Link to Official Course Descriptor.

Pre-requisite course(s): F70LA Life Insurance Mathematics A .

Location: Edinburgh, Malaysia.

Semester: 2.

Learning Outcomes: Subject Mastery

At the end of studying this course the students should be able to do or understand the following:

  • derive Thiele’s differential equation for standard insurance benefits, and solve it numerically using an Euler scheme
  • define Markov life-history models in terms of states, transitions and transition intensities
  • state and prove Kolmogorov’s forward equations, state Thiele’s differential equations, and use an Euler scheme to solve both numerically, for a general Markov multiple-state model
  • calculate risk reserves for simple homogeneous life insurance portfolios
  • define models for the joint life histories of two individuals; (a) as a multiple-state model; and (b) in terms of random future lifetimes
  • calculate expected present values, premiums and policy values for the following types of joint-life policies: first-death and second-death assurances and annuities, reversionary annuities, and contingent assurances
  • describe the main features of disability insurance, long-term care insurance and defined-benefit pension schemes
  • understand possible sources of heterogeneity, its effect on the analysis of insurance data, and its possible impact on insurance business
  • construct single figure indices to summarise mortality and other experiences, and understand the strengths and weakness of each
  • calculate the profit vector, profit signature, net present value, profit margin, discounted payback period, and internal rate of return for conventional policies
  • describe the effect on the profit vector of changes in the premium, valuation, and experience bases
  • describe the operation of the unit price and the charging structure for unit-linked policies
  • calculate the unit fund, sterling fund, sterling reserve, and measures of profit for unit-linked policies

Reading list:

  • Formulae and Tables for Actuarial Examinations
  • Introduction to Survival Models, Volumes 2 and 3 Hardy, Macdonald, Waters and McCutcheon.

Assessment Methods: Due to covid, assessment methods for Academic Year 2021/22 may vary from those noted on the official course descriptor. Please see:
- Maths (F1) Course Weightings 2021/22
- Computer Science (F2) Course Weightings 2021/22
- AMS (F7) Course Weightings 2021/22

SCQF Level: 10.

Credits: 15.

Other Information

Help: If you have any problems or questions regarding the course, you are encouraged to contact the course leader.

Canvas: further information and course materials are available on Canvas