The objectives of the assignment are to allow you to

•    Examine and employ a variety of exposed to risk, graduation and mortality projection techniques.

•    Develop an understanding of aspects of the theory and practice of statistical learning methods.

Context

You are currently working as an Actuary in the Australian Government focusing on providing advice about retirement income policy. The government is especially concerned with the future costs         required to fund various retirement schemes such as the Age Pension and has been investigating a number of different avenues to help to alleviate the problem.

Your team has recently been assigned to examine the viability of an alternative to the current superannuation scheme where

•    Individuals pay into a government regulated pool of funds during their working life.

•    Upon retirement, individuals are provided with a life annuity that will cover their living expenses until their death.

As a part of producing financial projections for this product, you haven tasked with coming up with appropriate mortality assumptions by generating a set of future life tables.

The task

You will be using the Australian mortality data on the Human Mortality Database in order to produce your mortality model. You can assume that this data has been suitably cleaned for obvious errors,     such as missing values.

Reminder: In order to access the HMD database, please use the login and password provided in the seminars. R packages such as demography that can help you manipulate the data have been             demonstrated in class. If you need more information, data documentation can be found on the        mortality.org website.

Modelling specifications

•    You should use the mortality data for the entire population, although you are welcome to examine the data split by gender as well if you think it will provide interesting insights.

•    You should produce a mortality model for all adults (18+).

•    If you have justifications for adjusting the data in a certain way (e.g. removing the earliest years, manually adjusting outliers, capping the maximum age at a certain point), you are  able to do so as long as you provide reasoning.

Your manager has asked you to prepare a mortality report with the following page limits (these are hard limits, any exceedances will not be marked!), consisting of the following sections:

1. Introduction (1 page)

a.    Provide a short introduction of the modelling problem and context

i.   You can include some references and research here if it assists in summarising the retirement income issues in Australia

b.    Provide a brief description of the data including the available variables, along with the range of these values.

2. Preliminary data analysis (1 page)

a.    Produce plots of mortality using the latest year in the data set

b.    Describe the curve you have plotted in part a, noting any points of interest. If          possible, providing explanations for these identified areas of interest with external references if appropriate.

3. Parametric curve fitting – Spline models (5 pages)

a.    Fit a natural cubic spline to the mortality data in the following way:

i.    Using the 2017 data as the calibration data and the 2018 data as the            validation data choose whether or not to place a knot at ages 5, 15, 25, 35, ..., 95.

1.    Hint: This means you will have to test 1024 models.

b.    Fit a smoothing spline to the mortality data using the 2017 data as the calibration    data and the 2018 data as the validation data in order to choose the optimal tuning parameter.

i.    Hint: Refer to the example in the lectures.

c.    Compare the performance of the two models on the 2019 data and provide concise remarks on the similarities and differences between the two approaches.

d.    For the superior model identified in Part c, Apply the following 6 tests of graduation to your fit on the 2018 data and provide conclusions as to whether the graduation is suitable :

i.   Chi-squared test of fit

ii.   Standardised deviations test

iii.   Signs test

iv.   Cumulative deviations test

v.   Grouping of signs test

vi.   Serial correlations test

vii.    In the above tests, for any cases where the graduation was not suitable, explain graphically or otherwise why this may have been the case.

e.    Describe any shortcomings of the model for our modelling purpose/context.

4. Mortality projection fitting – Lee-Carter Model (2 pages)

a.    Provide a brief description of the Lee-Carter model, including a concise explanation of the parameters.

b.    Fit the Lee-Carter model to the data up to year 2018.

c.    Report the average test error of projections using the Lee-Carter model for year 2019.

d.    Produce plots for the parameters of the Lee-Carter model and explain the interpretations of these plots.

5. Model comparison (2 pages)

a.    Produce projected mortality rates to the year 2030, 2040 and 2050 for both models and compare the results (graphically or otherwise). For the spli ne model, you can    assume that there are no mortality improvements.

b.    Discuss the implications of not including mortality improvements in the new          proposed scheme. If it is helpful, you may reference external materials to back up your arguments.

c.    Discuss any potential improvements that could be made to the models.

In a separate file submission, please also submit your R code as one script. This will also be                assessed for readability and reproducibility (please, for example, provide comments throughout your code to explain the script).

Note that the page limits are to give some guidance as to the maximum amount you should need to write. If you are able to concisely express all the key relevant ideas in less space, this will be viewed more favourably.

If you have any questions about the assignment, please post your questions to the discussion forums on iLearn.

Marking rubric and assessment

Your assignment is weighted 30% towards your final result for ACST3059/8086. The marking rubric on the following page indicates the criteria for the evaluation of your mortality report. You will be  awarded a percentage grade for each criterion. From these grades, your result out of 30% will         automatically be calculated. Your results will be available when you click your submission on the    iLearn website.

Academic Honesty and Referencing

Academic honesty means that you act with integrity in the creation, development, application and use of ideas and information1 . This means that:

•    All academic work claims as original is the work of the author making the claim;

•    All academic collaborations are acknowledged;

•    Academic work is not falsified in any way; and

•    Where ideas of others are used, these ideas are acknowledged appropriately.

Your assignment submission should be your own work, written in your own words. (Your report can also use tables or figures to summarise your research or main conclusions). This includes your R         script. The software Turnitin will be used to check for overlap with other published or student work. Penalties for plagiarism can be very severe.

You should clearly acknowledge any sources of information that you use by citing the information at the appropriate place in your text. You can do this by inserting an endnote at the appropriate place   in your text and then listing all of your numbered endnotes with the full details of each reference on the reference page at the end of your mortality report. Alternatively, you can provide the author and year of the reference at the appropriate place in your text, e.g.

The issue was first raised by Hyndman et al. (2013).

and then list the full details of each of the references on your final page reference list.

Use the following examples to guide you as to how to list references on your reference list: Hinde, A. (1998). Demographic Methods. Hodder Arnold Publication, London, UK.

Hollmann, F. W., Mulder, T. J., and Kallan, J. E. (1999). Methodology & Assumptions for the Population Projections of the United States: 1999 to 2010. US Department of Commerce, Bureau of the Census, Population Division, Population Projections Branch.

Human Mortality Database (2016). University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Retrieved from http://www.mortality.org, accessed on 21      July 2016.

For any other references, use a reasonable format that provides all relevant information including author(s), year of publication, title of publication, etc. It is up to you to decide how to format your list and we simply require you to be clear and provide enough information to fully specify the        reference.

Submission details

Deadline: Week 8, Sunday 2nd October, 11:59pm (Submit earlier than this in case of technical issues!) You may resubmit your file as many times as you like.

Format: Your report should be a PDF file, submitted via Turnitin.  Your R script should also be submitted as a separate file.

Filename: Please follow this convention exactly when naming your submissions

• 12345678SmithBobReport

• 12345678SmithBobRcode

• Student ID: 12345678

• Last Name: Smith

• First Name: Bob

• File title: Report or Rcode

Submission: To submit your files, click on the Assignment Submission link on the iLearn                  webpage.  Under the “My Submissions” tab, fill in a “Submission Title” (use “Assignment”) and    submit your report and code by attaching your files through “File to Submit” in Part 1 and Part 2.

Please note that Turnitin graded assignments can take up to several hours to upload when the        system is busy, particularly near deadlines when many students are submitting. Please allow for this by not submitting your assignment too close to the deadline.