STAT 6058 - Risk Modelling 2
Assignment
Semester 2 - 2023
Total Marks:
For STAT 6058 students 90 marks.
Notes:
1. No late assignments will be accepted. If extension is required, you need to
contact the lecturer NO LESS THAN 24 HOURS before submission time.
2. The assignment data is provided in an Excel spreadsheet and requires you
to submit the ‘filled out’ Excel spreadsheet under ‘Part 2’ of the Turnitin
tool. You MUST include your answers in the required space provided. You
can add as many worksheets as you would like. If you use R for any part of
the question, submit the R code under ‘Part 3’ of the Turnitin tool. All your
answers should be reproducible, with appropriate direction provided in your
answer script, in the form of:
• Please see worksheet XYZ in the spreadsheet
• Please run lines 1-10 of the R code provided to generate results.
3. Name your Answer script and Excel file starting with your University ID.
4. Assignments that are not accompanied by a COMPLETED Assignment
cover sheet will get a grade of 0.
1
Information
See the accompanying spreadsheet "Assignment 3 - Question.xlsx" on Wattle
to be used for this question.
You are a senior actuarial analyst working in the Reserving Team at WC Insurance
Limited ("WC Ltd"). WC Ltd is an APRA authorised general insurer specialising in
workers’ compensation insurance in the fictitious Australian state of Rictoria. In this
state, workers’ compensation insurance is privately underwritten, and insurers have much
discretion in designing their products.
WC Ltd offers a workers’ compensation product that provides three types of benefits:
• Weekly payments ("WKY"): Income replacement to compensate for loss of earnings
while injured. WC Ltd will compensate the injured worker at 80% of their salary
payable until retirement at aged 65 or when the worker is no longer incapacitated.
• Medical payments ("MED"): Hospital costs and ongoing care and treatment costs
such as surgery, doctor visits, medicine, rehabilitation and attendant care services.
There are no limits to Medical benefits.
• Lump sum payments ("LMS"): Compensation for permanent impairments and
death entitlements.
WC Ltd has a 31 December balance date. The Business Intelligence Team has been
busy over the New Year preparing the data, including performing reconciliations and
data checks. It is 2 January 2020 and the valuation data has just been signed-off for the
Reserving Team to commence their 31 December 2019 liability valuation. The results of
the valuation are intended to be fed into WC Ltd’s financial statements.
For the purposes of the valuation you can assume:
• Historical inflation to 31 December 2019 has been 1.5% p.a. and future inflation is
assumed to be 2.5% p.a.;
• The risk free discount rate is 2% p.a.; and
• A risk margin of 20% gives a 75% Probability of Sufficiency.
Note in all valuation below, inflation should be allowed for where applicable.
2
1. (a) (7)Given the information in the “Claims file” worksheet, perform five data sense
checks. In your answer script, list the check, and after performing the check,
list any anomalies you have found that require further investigation and adjust-
ments/actions you would take to fix any errors uncovered.
Define Accident period as the half-year of injury (the two half years in a year are 1
Jan to 30 June and 1 July to 31 Dec), Development period as the difference between
injury half-year and payment half-year.
Define a claim as active in a six-month period if it has had a Medical payment in
that period.
Without adjusting the raw data for any errors or anomalies:
(b) (15)Create the active claim number and claim payment triangles for Medical
payments by accident and development period.
(You need to show your work for all the relevant parts above in the form of either
additional worksheet(s) or R-code, and include the two final triangles in your answer
script.)
This question is worth 22 marks.
3
2. The historical annual premium data is provided in the worksheet “Premium”.
(a) (2)Apportion the premiums in each half-year to match the accident period. Report
the apportioned premiums and list any assumptions you make in the answer
script.
Assume that there will be no further claims or payments after development half-year
25.
(b) Using the Payments Per Active Claim (PPAC) method (same as the PPCI
method):
i. (3)For claim numbers, calculate development factors for
• All periods
• Last 10 year ‘average’ (where full data is available)
• Last 5 year ‘average’ (where full data is available)
• Last 2 year ‘average’ (where full data is available)
• Last 1 year ‘average’ (where full data is available)
The selected development factor is the maximum of all your calculated fac-
tors. Report all the development factors as well as the selected factors in
the answer script.
ii. (3)Discuss the appropriateness of this method of selecting development factors
and any alternatives you should consider, with appropriate justification.
iii. (2)Calculate the ultimate claim numbers for the half-years 2007H1-2019H2,
and state them in the answer script.
iv. (2)Using the inflation data provided, adjust the medical claim payment amounts
to 31 Dec 2019. Report the inflation adjusted payment triangle in the answer
script and state any assumptions used.
v. (3)Calculate the PPCI factors (to 4 decimal places) for:
• All periods
• Last 10 year average (where full data is available)
• Last 5 year average (where full data is available)
• Last 2 year average (where full data is available)
• Last 1 year average (where full data is available)
4
For the purpose of this calculation, assume claims are fully run-off by de-
velopment half-year 18. For any later development half-year (until j = 18)
that have 0 payment values, the PPCI factor is assumed to be the same as
the PPCI factor from the latest development half-year. Report the PPCI
factors for j = 0 to 18 in the answer script.
You decide to use the average of the PPCI factors of the ‘Last 5 year average’,
‘Last 2 year average’ and ‘Last 1 year average’ until development half-year 18
and a value of $0 thereafter to forecast future PPCIs. (If the PPCI factor of the
‘Last 5 year average’ is not available, use the average of the other two factors.)
vi. (3)Calculate the 75% probability of sufficiency outstanding claim reserves for
medical payments. State the total raw reserves, the total inflated and dis-
counted reserves, and the 75% probability of sufficiency outstanding claim
reserves in the answer script.
(c) (14)Calculate the 75% probability of sufficiency outstanding claim reserves for medi-
cal payments using the Bühlmann-Straub credibility model. You should consider
the premium data provided. To use the premium adjusted method, we assume
a common mean loss ratio for each accident year, and do the Bühlmann-Straub
calculations on the triangle of claims divided by earned premiums.
The development factors selected should be the ‘average’ claim development
factor from all periods.
In your answer script, state the following results:
• The triangle of claims divided by earned premiums.
• The selected development factors fˆ ∗j .
• The estimated common mean loss ratio µˆ.
• The raw oustanding claims from each accident year.
• The final discounted future claim payment triangle.
• The 75% probability of sufficiency outstanding claim reserves for medical
payments.
(You need to show your work for all the relevant parts above in the form of either
additional worksheet(s) or R-code. If you get a ‘Divide by Zero Error’ for later
5
development periods in the calculation of s2i . You can ignore them as the claims are
fully run-off by development period 19.)
This question is worth 32 marks.
6
3. Your boss, Jim Lee (the Appointed Actuary of WC Ltd), has asked you to estimate
the outstanding claims liabilities for the Medical payments. He wants the recent
changes to medical treatment to be explicitly captured in your estimates. He has
provided you with the following information.
Historically, i.e. as at 31 December 2018 (starting from 1 January 2011), there
has been 547 active Medical claims every half-year on average. From 1 January
2019, Rictorian hospitals and clinics rolled out a new medical treatment designed
to reduce the number of active Medical claims. Specifically, those administered the
new medical treatment have a probability of 25% to recover at the end of six months
of treatment. However, this new treatment is on average 25% more expensive than
current procedures. The current medical treatment costs are approximately $6,700
per patient every six months. This new treatment would be rolled out in several
stages over a two-and-a-half-year period as displayed in the following table.
Period % of patients administered new treatment
1 Jan 19 - 30 Jun 19 20%
1 Jul 19 - 31 Dec 19 40%
1 Jan 20 - 30 Jun 20 60%
1 Jul 20 - 31 Dec 20 80%
1 Jan 21 - 30 Jun 21 100%
(a) (10)State whether you expect the number of active claims and PPAC to increase or
reduce, and explain why. Then, quantify the percentage impact that the new
medical treatment is expected to have on the following over each of the next six
half-years:
i. Active claims
ii. Payments per active claim.
For this calculation, you should ignore the recovery from the current treatment.
You may want to use the table header provided below as a starting point.
Period Medical Active Claims Payments Per Active Claim
Expected
Number
of Active
Claims
Claims
with
New
Treat-
ment
Claims
with
Current
Treat-
ment
Expected
Healed
from New
Treat-
ment
%
change
in Ac-
tive
Claims
PPAC
New
Treat-
ment
PPAC
Current
Treat-
ment
Expected
PPAC
% change in
PPAC
7
(In part (a), you do not need to use any additional information than that provided
in question 3.)
(b) (8)Analysing active claims and PPAC in Question 2 by payment half-year, com-
ment on how the actual experience for 2019H1 and 2019H2 compare to your
expectations in Question 3(a). Include any charts/tables in your response as
well as any limitations of your analysis.
(PPAC for a certain payment half-year is defined as total medical payments from
that half-year divided by the total number of active claims from that half-year.)
(c) (13)Detail the modifications you would make for active claims and PPAC to allow
for the new treatment. Clearly discuss the expected impact of these changes on
your projections, and any sense check(s) that you may conduct.
You do not need to implement the changes.
(d) (5)FOR STAT 6058 students only. Using appropriate data, discuss the validity
of the claim that there there has been 547 active Medical claims between 2011
and 2018 every half-year.
This question is worth 36 marks.