SOA Exam ASTAM Fall 2023, Question 5
Study guide: Exam ASTAM
An insurer has a portfolio of one-year policies with annual premiums. The claims triangle below shows the incremental claim payments for the portfolio for each of the last four accident years, by development year. Assume all incremental payments are made at the middle of each year, and claims are fully developed by the end of Development Year (DY) 3.
| Accident Year (AY) | DY 0 | DY 1 | DY 2 | DY 3 |
|---|---|---|---|---|
| 2019 | 104 | 38 | 17 | 5 |
| 2020 | 106 | 40 | 19 | |
| 2021 | 138 | 45 | ||
| 2022 | 145 |
You are given the following inflation rates, measured from mid-year to mid-year:
| Period | Inflation |
|---|---|
| 2019-2020 | 2.0% |
| 2020-2021 | 4.4% |
| 2021-2022 | 7.5% |
| 2022-2023 | 3.0% |
Part a (1 point)
Show that the AY 2019 inflation-adjusted aggregate paid claims, expressed in terms of mid-2023 monetary units, are 190 to the nearest 10. You should calculate the value to the nearest 0.1.
Part b (3 points)
Using the inflation-adjusted chain ladder method, show that the estimated total ultimate claims from all four accident years of the table, expressed in terms of mid-2023 monetary units, is 840 to the nearest 10. You should calculate the value to the nearest 0.1.
Part c (3 points)
You are given that the total earned premiums were:
| Year | Earned Premiums |
|---|---|
| 2019 | 220 |
| 2020 | 225 |
| 2021 | 235 |
| 2022 | 275 |
Between 2018 and 2023 there were only two premium rate increases:
- A 4% increase on 1 July 2020
- A 6% increase on 1 October 2021
It is assumed that policies are issued uniformly and premiums are earned evenly over each year.
Show that the total earned premium for 2019-2022 at current rate levels is 1020 to the nearest 10. You should calculate the value to the nearest 0.1.
Part d (1 point)
You are also given the following information:
(i) Total inflation-adjusted fixed expenses of 35 were incurred during 2019-2022.
(ii) Variable expenses are included in the run-off triangle figures.
(iii) The permissible loss ratio is 0.8.
Calculate the percentage increase in premium using the loss ratio method.
Part e (1 point)
State with reasons whether the year 2019 earned premiums adjusted to current rate level would increase, decrease, or stay the same if the policies were all issued in the first three months of 2019. Assume that the unadjusted 2019 earned premiums remain at 220.
Answer this question and see the worked solution