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STAT 6058 - Risk Modelling
Assignment
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)