Example 9: Bootstrapping from Development
Triangles
Number of Years
Resamples
FirstYear
Den L2
First Yr to Sample
Smoothing
Yrs to Sample
Triangle
Results of triangle analysis for a Simulated Triangle
Click Compute to see results...
Notes
Input: number of years (or quarters) in the triangle, the first year,
the first year to sample (1 is the most recent year) and the number
of years to sample.
Model resamples link ratios from the triangle to determine a
distribution of Factors-To-Ultimate (FTU).
Resamples text box
controls the number of resamples.
Den_L2 controls the size of
the bucketted distribution.
Smoothing controls whether any smoothing
is applied to the simulated FTU distribution. Does not
work well the the Commerical Auto triangles.
Model shows shifted lognormal fit to the bootstrap sample. This is
generally a very good fit.
Model uses the shifted lognormal fit to determine confidence intervals
around the standard link-ratio ultimates. These are shown below the graphs.
There are four built-in triangles: industry schedule P for commercial auto
liability, paid and incurred; a triangle related to
reinsurance data; and the triangle from Greg Taylor's
papers on the evolution of loss distributions.
References
Mildenhall, S., "Bayesian-Bootstrap Loss
Development" CAS DFA Seminar Presentation, July 1999.
Ostaszewski K. and G. Rempala "Applications of
Resampling Methods in Dynamic Financial Analysis"
1998 CAS DFA Call Papers, CAS (1998). Available on the CAS Website.
Taylor, G. "Development of an incurred loss distribution
over time" COTOR Working Paper, 1998
Efron, B. and R. Tribshirani, "An Introduction to the Bootstrap" Chapman & Hall (1993)