Chain Ladder Method
From the previous introduction, we have known the definition of IBNR reserves.
In this section, I will introduce three methods to estimate the IBNR reserves from the run-off triangle.
Run-off Triangles
When we wang to estimate the reserves prepared for the claims that have occurred but have not been reported, one of the most common methods is to use the run-off triangles. The run-off triangle is a matrix that shows the development of the claims over time.
| Development year | ||||
|---|---|---|---|---|
| Origin year | 0 | 1 | 2 | 3 |
| 2020 | 100 | 180 | 240 | 280 |
| 2021 | 120 | 220 | 300 | |
| 2022 | 140 | 260 | ||
| 2023 | 160 | |||
From the above table, We can find several important information:
- Origin year (Policy year): the year in which the claim occurred.
- Development year: the year in which the claim was reported relative to the origin year.
- Cliams: the cumulative number of claims reported from the origin year to the relative development year.
Question
If we assume that all claims are settled within three development years, the main question is:
what is the IBNR reserve for all origin years according to the above run-off triangle?
Solutions
To estimate the IBNR reserves, we can have three different methods via the run-off triangle:
Three methods will be introduced in the following sections.