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- 首页 >> CS 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 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.
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 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.