I am very pleased to see that several actuaries have read my previous posts. This week I am going to look at how SAS can be used to very efficiently, accurately and quickly produce simple actuarial reserve estimates using the chain ladder method. In this particular example I am going to use a volume 12 weighted chain ladder but the code can be easily adapted to use other methods or to remove outlying development factors.
So the first thing I need to do is create an example loss triangle. I’ve set the triangle to have 36 rows and columns. This could be 36 months, quarters or years depending on the granularity being used in the reserving but I am going to refer to them as months. For each origin month I have set the first development month’s incurred to be £10,000 multiplied by 1 plus a random number between 0 and 1. The following development months are generated using random numbers set up in a way that it mimics the behavior of a short tail class of business.
Next I turn the loss triangle into a cumulative triangle and add a column with the paid to date.
So having created an example loss triangle that has characteristics similar to a real loss triangle I need to calculate the development factors. This is done by creating a temporary dataset containing the sum of the relevant lines from each of the columns. Then ratios of these sums are fed into global variables.
In the next step I have chosen to complete the triangle by applying the development factors. It is just as easy to calculate cumulative development factors but by completing the triangle it is available for further analysis for example actual vs expected monitoring.
So as a final step we calculate the reserve for each month and then sum the ultimate, reserve and paid.
So this code will produce a simple reserve estimate by using the volume 12 weighted chain ladder method. The code can be easily adapted to use other methods including boot strapping or a BF method. Further it would be straight forward to convert into a stochastic method and generate a distribution around the reserves through simulations of the development factors. As an extension machine learning could be used to analyse the claims development and locate the granular development that best reproduces the behavior of an out sample of data.
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