THE UNIVERSITY OF MELBOURNE
Centre for Actuarial Studies, Department of Economics
ACTL30002 Actuarial Modelling II
Assignment 1
COVER SHEET
Due by 5pm on Friday 12 April 2024
Instructions for submission
1. This assignment contributes 15% of the total university assessment in this subject. Please
follow these instructions carefully. Penalties will be imposed for failure to comply with
them.
2. All steps of calculation must be clearly shown. Explanatory notes on how you conduct
the calculation in your excel file is necessary. Your solutions do not have to be typed;
nevertheless, handwriting that is very difficult to read may not be marked. Please refrain
from using a red pen anywhere in the assignment.
3. Please indicate your student ID number clearly in your file names, e.g., idnumber.pdf and
idnumber.xlsx
4. Attach this cover sheet in front of your solutions, and then submit solutions in PDF format
together with your programming file and/or Excel spreadsheet to Canvas before the due
date.
5. Penalties will apply to any late submissions. If you are unable to submit on time, please
contact FBE to make an official application for late submission.
6. If you have any questions about this assignment, please post them to LMS under the tag
of “Discussions”. Assignment-related questions send to me via email will not be answered.
7. This is an individual assignment. Please sign below to declare that your work does not
involve plagiarism or collusion.
I declare that this assignment is my own work and does not involve plagiarism or collusion
with other students.
Student Number Name in full Signature Number of sheets submitted
Plagiarism is the presentation by a student of an assignment which has in fact been copied
in whole or in part from another student’s work, or from any other source (e.g. published books
or periodicals), without due acknowledgement in the text.
Collusion is the presentation by a student of an assignment as his or her own which is in
fact the result in whole or part of unauthorised collaboration with another person or persons.
1. (20 marks) You are the pricing actuary in a large life insurance company in Australia. Your
manager asked you to conduct a mortality investigation for the period from 1 January 2017
to 31 December 2017 based on the data collected by the claim management department
for a portfolio of term insurance policies (ACTL30002 Assgt1 data.xlsx).
In this data file, for each life insurance policy you can find its policy number, birthday of
the life insured, sum insured, policy status at 31 Dec 2017 (NIF: not in force; IF: in force)
and the date of claim if any. All policies were IF on 1 January 2017.
(a) Making use of the policy and claims data provided:
i. Determine the central ETR values for age x next birthday, where x covers all
ages that have positive exposure values;
ii. Determine the initial ETR values for age x next birthday, where x covers all ages
that have positive exposure values;
iii. Construct a life table that covers EXACT ages 45-54. The table should at least
contain a column of age x and a column of qx.
To complete these tasks, you will need to use the exposed to risk method and make
assumptions when needed.
(b) Using the mortality rates obtained in part (a) and the expected mortality table given
in the data file, investigate whether the expected mortality table can be used to price
the given insurance portfolio or not. Note that you will need to choose appropriate
test methods and make assumptions whenever needed. Also think about whether
any information given in the data file might concern you during the process of your
testing.
Requirements:
• Submit a written document that contains the main results and necessary information
regarding the main steps/methods that you have used to obtain the results.
• Submit an Excel spreadsheet that contain senough details for checking.
2. (10 marks) In a mortality investigation from 1/7/2008 to 1/1/2010, let (x) be the total
number of deaths aged x nearest birthday at the previous 1st of July and let P(x)(t) be the
number of lives aged x last birthday on census dates 1 July 2008+t, for t = 0, 0.5, 1, 1.5.
Suppose that θ(40) = 30, θ(41) = 32, and population estimates at census dates are given
below:
t = 0.0 t = 0.5 t = 1.0 t = 1.5
P(39)(t) 2000 2100 2100 2000
P(40)(t) 2200 2200 2100 2200
P(41)(t) 2100 2100 2200 2000
(a) The Principle of Correspondence states that the age label for deaths must be the
same as that for the census when estimating mortality rates and, therefore, the census
population figure may require adjustment. What is the estimate of the population
aged 40 nearest birthday at 1/7/2008?
(b) What is the estimate of the population aged 40 nearest birthday at 1/1/2009?
(c) What is the average age at the start of the rate interval for deaths having age label
40?
(d) What is an estimate of the central exposed to risk in respect of lives aged 40 nearest
birthday, using the census method?
(e) Calculate an estimate of q40 to six decimal place. State any assumption made for the
calculation.
END OF ASSIGNMENT
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