This example shows how you might model the uncertainty involved in payment of insurance claims. To model this properly, you must account for the uncertainty in both the total number of claims and the dollar amounts of each claim made. This is done using the RiskCompound function.
Suppose that the company is required by law to have enough money on hand to pay all the claims with the probability of 95%, and that it can only set aside $2000 for the purposes of this particular insurance product. On the other hand, a simulation of the model shows that the 95th percentile of the Total Payment Amount is around $2700. Assume further that the company can purchase from a larger company an insurance policy against the number of claims being in the top decile. The policy under consideration specifies that if the number of claims falls within the top decile, the larger company will satisfy all the claims. The smaller company can model the situation with the policy in place by using Stress Analysis to stress the distribution for total number of claims from the 0th to 90th percentile. With the modified distribution the 95th percentile of the Total Payment Amount is reduced to around $1650. If the policy costs up to $350, the smaller company can purchase it and keep $1650 on hand to comply with the law.
Would the larger company be willing to sell the policy for under $350? There is a 10% probability that it will be required to make payments under the policy. The payments can be analyzed using the same model and stressing the distribution for total number of claims from the 90th to 100th percentile. This analysis shows the mean payment to be around $2800. Since there is only a 10% probability that claims will need to be satisfied, the mean cost to the larger company is around $280. Hence, it does not seem unreasonable for the larger company to sell the policy for $350.