ACST3059/8086 Actuarial Modelling – Individual Assignment 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 spline 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 b
ack 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. Section Criteria Weight Fail Pass Credit Distinction High Distinction Introduction An introduction to the modelling problem/ context and a brief description of the variables available for modelling 10% No introduction or description is provided An introduction or description are provided but with aspects are missing and/or poorly described An introduction and description are provided but a small number of aspects could be better improved. Both the introduction and descriptions are provided in a clear manner. All aspects of the introduction and descriptions are provided in a clear and concise manner. Preliminary Data Analysis A plot of Australian mortality in 2019 is produced and points of interest are identified. 10% No mortality plot is provided or points of interest are not identified. A mortality plot is provided and some points of interest are identified but insight is of poor quality or explanations are not provided. A mortality plot is provided and points of interest are identified with some explanations provided but the explanations could be more detailed. A clear mortality plot is provided and points of interest are identified along with valid explanations. A clear mortality plot is provided and points of interest are identified along with clear and concise explanations. Parametric Curve Fitting The spline mortality curves are fitted properly to the data with validation procedures and documentation. The graduation hypothesis tests are applied and their conclusions analysed. 40% The response lacks significant portions of the required components. The response fits the models but portions are missing from the documentation or graduation test components. Conclusions The response fits the models, provides some documentation and completes the graduation tests, but some conclusion are not justified in enough detail. The response adequately fits and validates the models, provides proper documentation and completes the graduation tests. The response adequately fits and validates the models, provides concise documentation and completes the graduation tests with Shortcomings of the approach are assessed. are not justified. Shortcomings are pointed out but not described well. Shortcomings of the approach are identified and described. excellent analysis of shortcomings, with most aspects of the modelling considered. Mortality Projection A concise description of the Lee-Carter model is provided, along with an accurate fit to the data. The model is tested to the right data set. Also, the parameters of the model are properly analysed. 20% The Lee- Carter model is not fitted to the data. The model is fitted to the data but the explanatory components provide insufficient detail. The model is fitted to the data and explanatory components and analysis are provided, but the analysis lacks detail or misses some points. The model is fitted and tested. Explanatory components and analysis are provided in some detail. The model is fitted and tested and the explanatory components and analysis of results are excellent with most aspects considered. Model Comparison Mortality rates are properly projected and the model results are compared and contrasted. Implications of mortality improvements are discussed and improvement suggestions provided 15% Mortality rates are not projected or implications are not discussed. Mortality rates are incorrectly projected or the implications are not discussed with sufficient detail. Mortality rates are fitted to the data with limited model comparison and discussion of the implications of mortality improvements. Mortality rates are fitted to the data with analysis that compares the model. Implications of mortality improvements are discussed in some detail. Mortality rates are fitted to the data with great comparison analysis. Implications and improvements are discussed with most aspects considered. R Code R code is provided in a readable/reproducible manner. 5% No R code is provided R code is provided but is missing some parts R code is provided along with comments but the structure or comments are unclear or could be improved. R code is provided and is structure ad commented well. Well structured R code is provided along with clear and concise commentary.