Actuarial Notes

SOA Exam ASTAM Sample Question 3

Study guide: Exam ASTAM

During 2021, AAA Insurance collects the following premium amounts:

Month January March May July
Premium Collected 1,600 1,800 1,200 1,200
  • All premiums are paid on the first day of the month and all premiums are annual premiums.
  • The unearned premium reserve at 31 Dec 2020 was 1,300.
  • The company expects a loss ratio of 80%.
  • During 2021, the company paid losses for claims incurred in 2021 of 2,500.

Part a

Use the loss ratio method to determine the outstanding claim reserve for accident year 2021 for this coverage that should be held on 31 Dec 2021.

Part b

The insurer has the following Paid Claims triangle for this coverage. There is no further development after year 5.

Cumulative Loss Payments by Development Year

Accident Year 0 1 2 3 4 5
2016 1,000 1,500 1,700 1,800 1,850 1,875
2017 1,100 1,750 1,775 1,825 1,870
2018 1,200 1,900 2,200 2,350
2019 1,500 2,200 2,500
2020 2,000 2,900
2021 2,500
  • (i) The loss development factor for the period from year 0 to year 1 is 1.51 to two decimal places. Calculate the loss development factor to five decimal places.
  • (ii) Calculate the outstanding claim reserve on December 31, 2021.
  • (iii) Determine the total amount of claims paid in 2021.

Part c

For the claims from accident year 2021, determine the reserves as of 31 Dec 2021 using the Bornhuetter-Ferguson method, where the prior estimate is the outstanding claim reserve using the loss ratio method.

Part d

Explain briefly one advantage and one disadvantage of the Bornhuetter-Ferguson method, compared with the Chain Ladder approach.

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