# F70LA Life Insurance Mathematics A

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

Aims:

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.

Summary:

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

## Detailed Information

Course Description: Link to Official Course Descriptor.

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.

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

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.

## 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