F70LA: Life Insurance Mathematics A

B.Sc. in Actuarial Science

Lecturer: Tom Fischer
Office: Colin Maclaurin Building, Room F.14
Tel: 0131 451 4371
Email: c.t.w.fischer@hw.ac.uk

News

• THIS MODULE PAGE WILL WITH IMMEDIATE EFFECT BE DISCONTINUED. PLEASE USE FROM NOW ON VISION TO GAIN ACCESS TO MODULE INFORMATION AND TEACHING MATERIALS.
• Sign up for the Burn here.
• Regarding the computer labs:
  Surnames starting with Mc-Z please come Tuesday, 1:15pm to SRG12/13/14.
  Surnames starting with A-Mb please come Wednesday, 9:15am to EC304.
  The labs this time will feature an introduction to Excel, and some first and easy LIM calculations.
• You should now be able to solve problems 1-11.

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

At the end of this 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.

Reading

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

Assessment

This module and F70LB (Life Insurance Mathematics B) are examined together in one 3 hour exam (80%) at the end of the 2nd semester. Each module has an Excel-based assignment (10% each).

Help

Downloads

• module guide
• RBS offer
• graph for the select period
  NOTE: This picture is a gross simplification. A more realistic picture would need to show a broader range of health for the 'average' crowd, and some sort of 'blurring' or 'widening' for the 'select' crowd as it moves downwards in time and joins back into the average crowd.
• The old "Green Tables" can be downloaded here.
• tutorial problems (up to No. 43)
  
• tutorial solutions (up to No. 9)
  
• AM92 q(x)
• How-to-spreedsheet
• 1st Spreadsheet, numerical solutions for 1st Spreadsheet (no formulae, numbers only)