**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,
- 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