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England and Verrall 2001 Table 6.1: chain-ladder reserve and ODP prediction error of a triangle with a negative increment
| Tool | Loss Reserving |
| Source | England, P. D., and Verrall, R. J. (2001). "A Flexible Framework for Stochastic Claims Reserving." Proceedings of the Casualty Actuarial Society, Vol. 88. Tables 6.1–6.3. |
| Level | Graduate |
Problem
An incremental run-off triangle of ten origin years with a negative increment in year 3 at delay 3 is given. Convert it to cumulative form, estimate the chain-ladder development factors and the reserve of every origin year, and estimate the prediction error of each reserve and of the total by bootstrapping the over-dispersed Poisson model.
Inputs to Enter
- Incremental triangle loaded from the selector (first row 45,630, 23,350, 2,924 … 621; cell (3,3) = −1,854; last row 76,013)
- Volume-weighted factors, no tail; ODP bootstrap with gamma process error
Answers
- Development factors (Table 6.2) 1.4906, 1.0516, 1.0419, 1.0268, 1.0254, 1.0149, 1.0130, 1.0067, 1.0078
- Reserves (Table 6.3) years 2–10: 683, 1,792, 4,363, 5,657, 8,209, 10,914, 15,199, 21,135, 60,335; total 128,286
- ODP prediction error: total 15 %, year 10 17 %, year 9 24 %, year 5 50 % (the tool's bootstrap agrees within a few points)
Notes
Choose the England–Verrall 2001 example in the selector; the triangle type is set to incremental so the negative cell is kept.