School of Mathematical and Computer Sciences

F70LA Life Insurance Mathematics A

Lecturer: Tom Fischer

Aims

This module 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,
• Thiele's differential equation and its numerical solution.

Learning outcomes

By the end of the module 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;
• derive and explain Thiele's differential equation in the two-state continuous-time model;
• use an Euler scheme to solve Thiele's differential equation numerically;
• use the Central Limit Theorem to show why risk reserves are needed, and to calculate risk reserves for insurance portfolios of different sizes;
state and prove Lidstone's theorem, and use it to describe the traditional with-profits model of implicit risk reserving.

Prerequisites

F72ZB2 and F72ZD3.

Reading

• Formulae and Tables for Actuarial Examinations (Yellow Tables)
• Introduction to Survival Models, Volumes 1, 2 and 3 by Hardy, Macdonald, Waters and McCutcheon

Assessment

Life Insurance Mathematics A is assessed in combination with Life Insurance Mathematics B. Each has a project contributing 10% to the total mark, and there is a single 3-hour written exam contributing 80% to the total mark at the end of semester 2.

Help

If you have any problems or questions regarding the module, you are encouraged to contact the lecturer.

Module web page

Further information and course materials are available on Vision or at http://www.ma.hw.ac.uk/~fischer/