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ACTL30002 Actuarial Modelling II
Assignment 1
COVER SHEET
Due by 5pm on Friday 11 April 2025
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
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Name in full
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Signature
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Number of sheets submitted
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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 2025 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, date of entry, date of withdrawal, and the date of claim if there is any.
(a) Making use of the policy and claims data provided:
i. Determine the central ETR values for age x last birthday, where x covers all ages that have positive exposure values;
ii. Determine the initial ETR values for age x last birthday, where x covers all ages that have positive exposure values;
iii. Construct a life table that covers EXACT ages 44-54. The table should 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) Consider a mortality investigation from 1/7/2008 to 1/7/2010. Let θ(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, 1/10/2008 (t = 0.25), 1/4/2009 (t = 0.75), 1/10/2009 (t = 1.25), and 1/4/2010 (t = 1.75). Suppose that θ(40) = 30, θ(41) = 32, and population estimates at census dates are given below:
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t = 0.25
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t = 0.75
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t = 1.25
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t = 1.75
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P(39)(t)
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2000
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2100
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2100
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2000
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P(40)(t)
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2200
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2200
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2100
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2200
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P(41)(t)
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2100
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2100
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2200
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2000
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(a) State the rate interval for deaths with the age label of 40 and the average age at the start of the rate interval.
(b) 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.
i. What is the estimate of the population aged 40 at 1/10/2008 (t = 0.25) using the age label for deaths?ii. What is the estimate of the population aged 40 at 1/4/2009 (t = 0.75) using the age label for deaths?
(c) What is an estimate of the central exposed to risk for lives with the age label of 40 using the age label for deaths?
(d) Calculate an estimate of q40 to six decimal place. State any assumption made for the calculation.