Tools › Finance and Business › Insurance › Loss Reserving › Example
Friedland 2010: U.S. Industry Auto reported claims by development, expected claims, Bornhuetter–Ferguson and Cape Cod
| Tool | Loss Reserving |
| Source | Friedland, J. (2010). Estimating Unpaid Claims Using Basic Techniques. Casualty Actuarial Society, Arlington, VA. Chapter 7 Exhibit I, Chapter 8 Exhibit II, Chapter 9 Exhibit I and Chapter 10 Exhibit I. |
| Level | Professional |
Problem
The U.S. Industry Auto reported-claims triangle (accident years 1998–2007 at 12 to 120 months) is given with earned premiums and a priori claim ratios of 75 % for 1998–2002 and 65 % for 2003–2007. Select development factors from the usual averages, project the ultimate claims and the IBNR by the development method, then by the expected-claims, Bornhuetter–Ferguson and Cape Cod methods, and compare them.
Inputs to Enter
- Reported triangle loaded from the selector (1998 row 37,017,487 … 47,742,304; 2007 row 48,853,563), ages every 12 months
- Premiums 68,574,209 … 95,176,240 with claim ratios 75 % (1998–2002) and 65 % (2003–2007), loaded as the exposure column
- Selected factors as the exhibit prints them: 1.164, 1.056, 1.027, 1.012, 1.005, 1.003, 1.002, 1.001, 1.000; tail 1.000
Answers
- Averages (latest 3 volume-weighted): 1.164, 1.056, 1.027, 1.012, 1.005, 1.003, 1.002, 1.001, 1.000; latest 5 simple 1.168, 1.058, 1.027, 1.011, 1.004 …
- Cumulative development factors 1.292, 1.110, 1.051, 1.023, 1.011, 1.006, 1.003, 1.001, 1.000; percent reported 77.4, 90.1, 95.1, 97.8, 98.9 … %
- Development method: ultimate total 569,172,456 (AY 2007 63,118,803), IBNR 25,690,869
- Expected claims: total 569,281,839, IBNR 25,800,252 (AY 2000 negative, −3,156,946)
- Bornhuetter–Ferguson: expected unreported AY 2007 13,981,773, ultimate total 569,091,348, IBNR 25,609,761
- Cape Cod: used-up premium total 781,488,943, expected claim ratio 69.5 %, ultimate total 570,800,677, IBNR 27,319,090
Notes
Choose the U.S. Industry Auto, reported example in the selector. The exhibit multiplies by cumulative factors rounded to three decimals, so the tool reproduces the printed ultimates to the unit only with the rounded factors; the paid triangle is a second selector entry (tail 1.002, ultimate total 572,041,099).