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Centre for Actuarial Studies, Department of Economics

ACTL30002 Actuarial Modelling 2

Question One (1+2+1+2=6 marks)

AAA Life Insurance Company is conducting an investigation into its customer age structure. The Excel file “Assignment1Q1data.xlsx” contains the customer ID, birthdays, and policy effective  dates.  Determine the age label  for each customer based on the  following  age definitions:

(a) At 1 January 2023, assuming all customers are alive, determine their age label based on “age last birthday.”

(b) At 1 January 2023, assuming all customers are alive, determine their age label based on “age last birthday at the previous policy anniversary.”

(c) At 1 July 2023, assuming all customers are alive, determine their age label based on “age next birthday.”

(d) At 1 July 2023, assuming all customers are alive, determine their age label based on “age next birthday at the previous policy anniversary.”

Question Two (2+4+5=11 marks)

Man Life is an insurance company which only sells life insurance to males. It has recently bought another smaller company called Mixed Life which sells business to both males and females. The company is reviewing the premium rates it charges for life insurance.

Man Life has records of the number ofpolicies in force at their year end, which is 31 December, recorded by age next birthday. Mixed Life has records of the number of policies in force on 31 December each year recorded by age last birthday for males and age nearest birthday for females.

These are the data for the most recent years.

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(a). Calculate the central exposed to risk of the combined portfolio for males aged 50 next birthday for the calendar year 2016, stating each assumption you make at the point where you make it.

(b). Calculate the central exposed to risk of the combined male and female portfolio for persons aged 50 next birthday for the calendar year 2016, stating each assumption you make at the point where you make it.

(c). By a careful review on the policy documentary, Mixed Lifejust realized that the previous record of date was wrong! The correct date should be 30 September in each year for both males and females. Calculate the contribution to central exposed to risk in (a) and (b).

Hint: This question is revised from Question 11 in CT4 2018 September exam at Institute and Faculty of Actuaries (IFoA, past exam papers with solutions can be foundhere), you are encouraged to borrow ideas from there.

Question Three (13 marks)

The excel “Assignment1Q3data.xlsx” contains deaths θx, initial ETR Ex, and standard table qx by age for lives between ages 0 and 80. Both deaths and initial ETR calculated are based on “age  last  birthday”  definition  of age.  Perform Chi-squared test, individual standardized deviations test, cumulative deviations test, signs test, runs test in Unit Two to compare actual death rates with those of the standard table and comment on the results.

Note: you need to combine the age groups such that the expected number of deaths is greater than or equal to 5; in chi-squared test, you should not use the approximation that px=1; the default significance level is 0.05; as for other testing specifications, such as the ranges in the individual  standardized  deviations  test,  the  age ranges  in  the  cumulative  deviations  test, whether or not to use normal approximation in runs test,  you are allowed to make appropriate decisions on your own but remember to present your specifications clearly in your descriptions and conclusions.