HERIOT-WATT UNIVERSITY
DEPARTMENT OF ACTUARIAL MATHEMATICS
AND STATISTICS
MSc/DIPLOMA IN ACTUARIAL SCIENCE
MSc IN ACTUARIAL SCIENCE AND
MANAGEMENT
F71AF
LIFE INSURANCE MATHEMATICS 1
Coursework: November 2020
Please submit your report on Vision no later than 3.15 p.m. on Friday 20
November, 2020.
Late submission incurs a penalty of 30% of the total mark awarded.
Your submission should consist of your written report, a print-out of your spread-
sheet(s), and the Plagiarism Declaration.
The University’s guide on plagiarism can be found at:
https://www.hw.ac.uk/students/studies/examinations/plagiarism.htm.
Your written report should not exceed five A4 pages in length (excluding the Course-
work Submission, Plagiarism Declaration and copies of print-outs, see next point).
Print-outs of your spreadsheet calculations should be provided as an appendix to
your report, with parameters clearly stated, columns clearly labelled and answers
clearly stated. You do not need to show every row of your spreadsheet.
40% of the available marks will be awarded for numerical accuracy, 20% will be
awarded for the structure of your report, and 30% for the writing and explanations
(see the marking rubric on Vision) and 10% will be awarded for the clarity and
layout of your spreadsheet.
This assignment counts for 30% of the total mark for F71AF.
1
You are the actuary responsible for calculating premium rates in a life insurance company.
Your company writes the following classes of business:
• term insurance with terms expiring at age 60;
• whole-life insurance; and
• whole-life insurance with the sum insured increasing continuously at rate 2% per
year.
In all cases, the sum insured is paid immediately on death and premiums are payable
annually in advance. The company will issue policies with sums insured of up to £100,000
without special underwriting procedures (in the case of increasing sums insured, an initial
sum insured of £100,000).
Until now, the company has charged the same premiums rates to smokers of cigarettes
(‘smokers’) and non-smokers of cigarettes (‘non-smokers’). The premium basis has been
3% per annum interest, no expenses, and a Makeham survival model with parameters
A = 3.555× 10−3, B = 6× 10−5 and c = 1.09.
In response to developments in the market, the company has decided in future to
charge different premiums to smokers and non-smokers. Unfortunately, there are no
reliable life tables for smokers and non-smokers. The best information available to you is
the following.
• The complete expectation of life of non-smokers age 30 is estimated to be 46.0 years.
• The complete expectation of life of smokers age 30 is estimated to be shorter than
that of non-smokers by the following number of years:
4 +
x
10000
where x is the last four digits of your student number. So, for example, if your stu-
dent number is H00012345, smokers have complete expectation of life 46−4.2345 =
41.7655 years.
You have decided to model the mortality of smokers and non-smokers using a Makeham
model with the same values of A and B as above, but different values of c such that the
estimated complete expectations of life are reproduced.
Question 1. Find the values of c that define your Makeham models for the mortality of
smokers and non-smokers.
Assignment continues on the next page . . .
2
As part of a systems upgrade, you have been asked to recommend suitable methods for
computing premiums for all types of business sold by the company, accurate to one pound
within its usual underwriting limits. (Policies with exceptionally large sums insured will
be treated individually.) The methods you recommend will be programmed into a system
that will automatically supply premium rate quotations to the company’s salespersons.
Question 2. Recommend suitable methods.
Your project submission should take the form of a written report explaining the steps
you have taken in choosing values of c in Q.1 and in choosing suitable methods in Q.2.
You should assume that the purpose of your report is that it will be kept as a written
record of the reasons for the decisions you have made so that they may be understood by
the company’s pricing actuaries in future years when any further systems development is
required. Therefore the clarity and precision of your explanations is very important.
END
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