Pricing |
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| Once you have set up a model for your data, it is a simple step to forecast for future underwriting (or accident) years and obtain all the information you need for pricing. The table below shows the mean (in black) and the standard deviation (in red) of the paid loss distribution for each future accident year and development period, as well as for accident year and calendar year totals. | |
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Distributions for accident year totals allow you to answer questions like "What is the probability that the loss ratio will exceed 100%?" with the proposed premiums. For example, in the graph to the right, if the premium for 1997 is $30M, there is a 3.3% probability that the losses will exceed the premium. All the information that is available about reserves - liability streams, percentiles, Value-at-Risk - is also available for future underwriting years. See Case Study 4 for an example of pricing excess of loss. |
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Comparing Paid Losses and Case Reserve Estimates |
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Comparing a model for the Paid Losses with a model for the Case Reserve Estimates can often give additional critical information
that cannot be extracted from the Incurred Losses triangle. Frequently we find that changes in the calendar trends in the Case
Reserve Estimates lag those in the Paid Losses, which will produce over- or under-reserving if you are relying on models for the
Incurred Losses. Occasionally there does not appear to be any relationship at all between the trends in the Paid Losses and those in the Case Reserve Estimates. See Case Study 2 for an example where the Case Reserve Estimates are telling a story that has nothing to do with the true reserves. |
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