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ChainLadder vignette: RAA triangle by Mack, the LDF exhibit with a 1.05 tail and the ODP bootstrap

ToolLoss Reserving
SourceGesmann, M., Murphy, D., Zhang, Y., Carrato, A., Wüthrich, M., Concina, F., and Dal Moro, E. (2024). "Claims reserving with R: ChainLadder package vignette." CRAN. MackChainLadder(RAA), the LDF exhibit and BootChainLadder(RAA).
LevelProfessional

Problem

The RAA reinsurance triangle (accident years 1981–1990, cumulative) is given. Compute the chain-ladder factors, the ultimate and IBNR of each year with Mack's standard errors, repeat the projection with a 1.05 tail factor, and bootstrap the over-dispersed Poisson model to obtain the mean, standard error and upper percentiles of the total IBNR.

Inputs to Enter

  • RAA triangle 1981–1990 loaded from the example selector (1981 row 5,012 … 18,834; 1990 row 2,063)
  • Volume-weighted factors over all years; tail none for the Mack run, entered tail 1.05 for the LDF exhibit
  • Bootstrap of the ODP chain ladder with gamma process error (R uses 999 resamples)
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Answers

  • f = 2.999, 1.624, 1.271, 1.172, 1.113, 1.042, 1.033, 1.017, 1.009
  • Ultimates 18,834 … 18,402; IBNR 1990 16,339.4, total IBNR 52,135.23 on a latest diagonal of 160,987; total ultimate 213,122.23
  • Mack S.E. 1990 24,566.3, total 26,909.01 (CV 0.5161); development to date 0.7554
  • With a 1.05 tail: cumulative LDF 9.366, 3.123, 1.923, 1.513, 1.292, 1.160, 1.113, 1.078, 1.060, 1.050; estimated ultimate total 223,778
  • Bootstrap (R, 999 resamples): mean IBNR 53,381, S.E. 19,144, 75 % 63,907, 95 % 88,138, 99 % 107,797; the tool's seeded bootstrap lands within its Monte Carlo tolerance (6–14 %)

Notes

Choose the RAA example in the selector; the first column of years is read as the labels. The bootstrap percentiles differ from R's by sampling error, not by method.

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