F70LA Life Insurance Mathematics A

Peter RidgesDr Larry O’Brien

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


This course aims:

  • to consider some more general models for mortality,
  • to introduce life insurance policies,
  • to introduce and develop the calculation of premiums,
  • to introduce and develop the calculation of policy values.


  • Selection and select life tables,
  • actuarial functions using ultimate and select life tables,
  • net and gross premiums,
  • equations of value,
  • impaired lives,
  • with-profits policies,
  • expenses and bonuses,
  • net and gross premium policy values,
  • recursive relationship between policy values.

Detailed Information

Pre-requisite course(s): F78AA Actuarial and Financial Mathematics A & F78AB Actuarial and Financial Mathematics B .

Location: Edinburgh, Malaysia.

Semester: 1.

Learning Outcomes: Subject Mastery

By the end of the course students should be able to:

  • demonstrate an understanding of select mortality rates;
  • construct a select-life mortality table;
  • derive financial functions for non-select and select lives;
  • express the variance of the present value of a stream of payments in terms of compound interest and life table functions, and evaluate the expression;
  • describe (for a single life) the cash flows implied by pure endowments, level annuities, level whole life, endowment, and term assurances;
  • derive expressions for the present value and accumulation of the contracts described above;
  • calculate financial functions for benefits payable more frequently than annually;
  • list the types of expenses incurred in writing a life insurance contract;
  • describe the different types of bonus on a with-profits contract;
  • calculate net and gross premiums for different types of life insurance and annuity contracts;
  • describe how reserves arise, under long-term insurance contracts covering mortality risk;
  • define the policy value as the expected future loss, and calculate the net and gross policy values for non-profit and with-profits contracts;
  • derive the recursive relationship between policy values at different durations, and use it to calculate policy values at non-integer durations.
  • Explain the concept of a survival model.
  • Derive the survival function from the definition of a random variable measuring the time until exit from a population.
  • Use the survival function to evaluate probabilities of events defined in terms of the time until exit.
  • Show how a survival table for integer values of x can be constructed using discrete rates of decrement.
  • Define the probability of survival, the radix of a single decrement table, and the survivorship group at duration t.
  • Define and develop relationships between the life functions l, q, p, d, mu and the expectation of life.
  • Describe the typical shapes of the curves for q, l and mu for human mortality.
  • Define the concepts of uniform distribution of decrements and a constant hazard rate, and use them to derive certain approximate relationships.
  • Write down expressions in terms of life table functions for the probability function of the curtate future lifetime and also the probability density function of the complete future lifetime of a life subject to a given life table.
  • Write down expressions in terms of simple life table functions for the mean and the variance of both the curtate and the complete future lifetime of a life subject to a given life table and evaluate these expressions in simple cases.

Reading list:

  • Formulae and Tables for Actuarial Examinations (Yellow Tables)
  • Actuarial Mathematics for Life Contingent Risks by Dickson, Hardy and Waters.

Assessment Methods:

Life Insurance Mathematics A is assessed in combination with Life Insurance Mathematics B. Each has a project contributing 20% to the total mark, and a written exam contributing 80% to the total mark.

SCQF Level: 10.

Other Information

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

VISION: further information and course materials are available on VISION