The CCDM Procedure

The SIMULATEDSYMBOL statement specifies one or more symbols and their associated probability distributions that you want PROC CCDM to simulate. You must use these symbols in the programming statements that define one or more of the ADJUSTEDSEVERITY= symbols. Hence, this statement is ignored if you do not specify the ADJUSTEDSEVERITY= option.

Each simulated symbol is a random variable that follows a specific parametric probability distribution, which you specify by using the distribution-name followed by a parameter-value-list that is enclosed in parentheses. The list of supported distributions is shown in Table 2 and Table 3 in the section Fixed Parameter-Value Distributions. The distribution-name is one of the names that appear in the Names column of those tables, and parameter-value-list is a comma- or space-separated list of numbers that represent the values of the parameters in the order in which the parameters appear top to bottom in the Parameters column for the specified distribution-name in those tables. The SIMULATEDSYMBOL statement can contain multiple such symbol specifications separated by a space.

The simulated symbols are useful in applications where your adjusted severity depends on some random variables that you have estimated externally. For example, if you are simulating the pure premium by specifying the SIMULATIONMODE=PP option, and if your frequency is modeled as the average number of claims per exposure, then to estimate the loss that you expect to pay for multiple exposures, you need to multiply the pure premium by the exposure. Typically, exposure is a random variable that you estimate externally by using a regression or time series forecasting technique. The SIMULATEDSYMBOL statement enables you to easily incorporate such stochastic variables in the simulation process. For example, if exposure denotes the exposure and if you have estimated it to follow a normal distribution , then you can specify the following statements to instruct PROC CCDM to estimate the distribution of the paid loss (paidLoss) that accounts for the randomness of exposure:

proc ccdm severitystore=mycas.sevstore countstore=mycas.cntstore
          simulationmode=pp adjustedseverity=paidLoss;
   simulatedsymbol exposure ~ normal(100,7.5);
   paidLoss = _sev_ * exposure;
run;