The HPCDM 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 parameters of your models. Any compound distribution estimate that is computed by using these uncertain parameter estimates is inherently uncertain. You can request that PROC HPCDM conduct parameter perturbation analysis, which assesses the effect of the parameter uncertainty on the estimates of the compound distribution by simulating multiple samples, each with parameters that are randomly perturbed from their mean estimates.

The following PROC HPCDM step adds the NPERTURBEDSAMPLES= option to the PROC HPCDM statement to request that perturbation analysis be conducted and the PRINT=PERTURBSUMMARY option to request that a summary of the perturbation analysis be displayed:

/* Conduct parameter perturbation analysis of
   the Poisson-gamma compound distribution model */
proc hpcdm countstore=countStorePoisson severityest=sevest
           seed=13579 nreplicates=10000 nperturbedsamples=30
           print(only)=(perturbsummary) plots=none;
   severitymodel gamma;
   output out=aggregateLossSample samplevar=aggloss;
   outsum out=aggregateLossSummary mean stddev skewness kurtosis
          p01 p05 p95 p995=var pctlpts=90 97.5;
run;

The Work.AggregateLossSummary data set contains the specified summary statistics and percentiles for all 30 perturbed samples. You can identify a perturbed sample by the value of the _DRAWID_ variable. The first few observations of the Work.AggregateLossSummary data set are shown in Figure 3. For the first observation, the value of the _DRAWID_ variable 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 HPCDM step produces the "Sample Perturbation Analysis" and "Sample Percentile Perturbation Analysis" tables that are shown in Figure 4. The tables show that you can expect a mean aggregate loss of about 4,098.5 and the standard error of the mean is 172.1. 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 16,448.2, but also the standard error of 708.9 to account for the effect of uncertainty in your frequency and severity parameter estimates.