It is important for an insurance company to estimate the amount of claims it will incur in a given year. This series of models assumes that there are three types of claims: auto, general liability, and worker's comp. Historical data for the company is included. The top section lists the numbers of claims for the previous 20 years. Summary measures across years are shown to the right. These include correlations, since it is conceivable that the number of claims of one type might be correlated with the number of claims of another type. The bottom section lists the claim dollar amounts for all claims in the most recent year. Summary measures for these are also listed to the right.
The base model assumes that the numbers of claims and the amounts of typical claims are known for the coming year, and that they are equal to the means of the historical data. For example, it assumes that there will be 994 auto claims, each for the amount $3,409. Then the total of all claims, shown in the red cell, is the sum of products of the values in rows 4 and 5. Of course, there is a lot of uncertainty in the values in rows 4 and 5, so later models that include this uncertainty are much more realistic than this deterministic model.
Additional models are included using the RiskCompound function to summarize claims, and resampling to deal with minimal historical data.