The CCDM Procedure

Continuing with the previous example, note that you have fitted the frequency and severity models by using the historical data. Even if you choose the best-fitting models, the true underlying models are not known exactly. This fact is reflected in the uncertainty that is associated with the estimates of your model parameters. Any compound distribution estimate that you compute by using these uncertain parameter estimates is inherently uncertain. You can request that PROC CCDM perform parameter perturbation analysis; this analysis assesses the effect of the uncertainty in parameter estimates on the estimates of the compound distribution by simulating multiple samples, each of which uses parameters that are randomly perturbed from their mean estimates.

The following PROC CCDM step adds the NPERTURBEDSAMPLES= option to the PROC CCDM statement to perform perturbation analysis and the PRINT=PERTURBSUMMARY option to display a summary of the perturbation analysis:

/* Perform parameter perturbation analysis of
   the Poisson-gamma compound distribution model */
proc ccdm countstore=mycas.countStorePoisson severityest=mycas.sevest
          seed=13579 nreplicates=10000 nperturbedsamples=30
          print(only)=(perturbsummary);
   severitymodel gamma;
   output out=mycas.aggregateLossSample samplevar=aggloss;
   outsum out=mycas.aggregateLossSummary mean stddev skewness kurtosis
          p01 p05 p95 p995=var pctlpts=90 97.5;
run;

The data table mycas.AggregateLossSummary contains the specified summary statistics and percentiles for all 30 perturbed samples. You can identify a perturbed sample by the value of the variable _DRAWID_. Figure 3 shows the first few observations of the data table mycas.AggregateLossSummary. For the first observation, the value of _DRAWID_ is 0, which represents an unperturbed sample—that is, the aggregate sample that is simulated without perturbing the parameters from their means.

The PRINT=PERTURBSUMMARY option in the preceding PROC CCDM step produces the "Sample Perturbation Analysis" and "Sample Percentile Perturbation Analysis" tables shown in Figure 4. The tables show that you can expect a mean aggregate loss of about 4,059 and the standard error of the mean is 190.1. If you want to use the VaR estimate to determine the amount of reserves that you need to maintain to cover the worst-case loss, then you should consider not only the mean estimate of the 99.5th percentile, which is about 16,224.5, but also the standard error of 700.2 to account for the effect of uncertainty in your frequency and severity parameter estimates.