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ACTL30002 Actuarial Modelling
Creation date：2024-05-24 17:16:03
Belonging category：会计Accounting
Actuarial Modelling
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ACTL30002 Actuarial Modelling 

COVER SHEET
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 on top of your solutions, and then submit your typed or scanned
solutions in PDF format together with your programming file and/or Excel spreadsheet
to Canvas by 5:00pm on Friday 21 April 2023.
5. I assume you already knew how to make a submission on Canvas. Please note that the
due time for this assignment is sharp. 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. I am not authorized to grant submission extensions.
6. If you have any questions about this assignment, please post them to LMS under the tag
of “Discussions”. Kindly note that I do not respond to assignment-related questions via
email.
7. This is an individual assignment. Please sign below to declare that your work does not
involve plagiarism or collusion among different students.
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
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.
Question One (1+2+1+2=6 marks)
AAA Life Insurance Company is conducting an investigation into its customer age structure.
The Excel file “Assignment1Q1data.xlsx” contains the customer ID, birthdays, and policy
effective dates. Determine the age label for each customer based on the following age
definitions:
(a) At 1 January 2023, assuming all customers are alive, determine their age label based on
“age last birthday.”
(b) At 1 January 2023, assuming all customers are alive, determine their age label based on
“age last birthday at the previous policy anniversary.”
(c) At 1 July 2023, assuming all customers are alive, determine their age label based on “age
next birthday.”
(d) At 1 July 2023, assuming all customers are alive, determine their age label based on “age
next birthday at the previous policy anniversary.”
Question Two (2+4+5=11 marks)
Man Life is an insurance company which only sells life insurance to males. It has recently
bought another smaller company called Mixed Life which sells business to both males and
females. The company is reviewing the premium rates it charges for life insurance.
Man Life has records of the number of policies in force at their year end, which is 31 December,
recorded by age next birthday. Mixed Life has records of the number of policies in force on 31
December each year recorded by age last birthday for males and age nearest birthday for
females.
These are the data for the most recent years.
Man Life
Age last Number of policies Number of policies Number of policies
birthday 31 Dec. 2015 31 Dec. 2016 31 Dec. 2017
49 4,789 4,296 4,367
50 4,953 5,009 4,809
51 5,300 5,186 5,902
Mixed Life Males
Age next Number of policies Number of policies Number of policies
birthday 31 Dec. 2015 31 Dec. 2016 31 Dec. 2017
49 1,832 1,650 1,698
50 1,800 1,750 1,550
51 1,966 1,756 1,569
Mixed Life Females
Age nearest Number of policies Number of policies Number of policies
birthday 31 Dec. 2015 31 Dec. 2016 31 Dec. 2017
49 1,602 1,568 1,639
50 1,506 1,497 1,508
51 1,610 1,587 1,411
(a). Calculate the central exposed to risk of the combined portfolio for males aged 50 next
birthday for the calendar year 2016, stating each assumption you make at the point where
you make it.
(b). Calculate the central exposed to risk of the combined male and female portfolio for
persons aged 50 next birthday for the calendar year 2016, stating each assumption you make
at the point where you make it.
(c). By a careful review on the policy documentary, Mixed Life just realized that the previous
record of date was wrong! The correct date should be 30 September in each year for both
males and females. Calculate the contribution to central exposed to risk in (a) and (b).
Hint: This question is revised from Question 11 in CT4 2018 September exam at Institute
and Faculty of Actuaries (IFoA, past exam papers with solutions can be found here), you are
encouraged to borrow ideas from there.
Question Three (13 marks)
The excel “Assignment1Q3data.xlsx” contains deaths θx, initial ETR Ex, and standard table
qx by age for lives between ages 0 and 80. Both deaths and initial ETR calculated are based on
“age last birthday” definition of age. Perform Chi-squared test, individual standardized
deviations test, cumulative deviations test, signs test, runs test in Unit Two to compare actual
death rates with those of the standard table and comment on the results.
Note: you need to combine the age groups such that the expected number of deaths is greater
than or equal to 5; in chi-squared test, you should not use the approximation that px=1; the
default significance level is 0.05; as for other testing specifications, such as the ranges in the
individual standardized deviations test, the age ranges in the cumulative deviations test,
whether or not to use normal approximation in runs test, you are allowed to make appropriate
decisions on your own but remember to present your specifications clearly in your descriptions
and conclusions.
Case category
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SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum
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