Modeling Uncertain Number of Events, Each with Uncertain Parameters
@RISK (risk analysis software using Monte Carlo simulation) is widely used in insurance and reinsurance for premium pricing and loss reserves modeling. A 2006 survey identified @RISK as the third most widely-used software by actuaries, after Microsoft Office and in-house actuarial tools.
@RISK‘s RiskCompound function allows for the sampling of frequency-severity distributions. This is often required in insurance modelling, as well as in some operations management situations. For example, to determine the total insurance claims payout, one must account for the uncertainty in both the total number of claims (frequency) and the dollar amount of each claim made (severity).
A powerful feature of the function is that the argument that corresponds to the severity may be a reference to a cell containing a formula (rather than just a single distribution function).
For example, one could use the function in the form RiskCompound(RiskPoisson(5), A10). The Poisson distribution would describe the frequency (occurrence) of events (e.g. an individual sample may determine that three events occur), and cell A10 would contain a formula that is separately evaluated for each of these three events (before returning the sum of these three as the sampled value of RiskCompound).
A simple example could be A10 = RiskLognorm(10000,1000)/(1.1^RiskWeibull(2,1)), with the Weibull distribution representing the time to settlement of an insurance claim, which is used to discount the basic claim value sampled from the Lognormal distribution of severity. For example, once a claim is filed for a nominal amount, the actual payment may be delayed due to court actions or disputes, which may reduce the cost of the claim to the insurer.