Two weeks ago I demonstrated a method of using SAS to simulate reserves. I noted in that post that simulating development factors has some drawbacks. For example the development factors are not independent and identically distributed and they are not likely to be uniformly distributed around the median value. In this post I will demonstrate a method of stochastic reserving which overcomes these drawbacks. This method is known as bootstrapping the over-dispersed Poisson distribution or ODP for short.
As ever this post is a demonstration of what can be done in SAS. It is not intended as a guide to reserving or a recommendation of one particular reserving method over another.
I am starting with a macro that generates an example loss triangle. This is slightly changed from last time because it includes a Proc summary to obtain the paid to date. Also I am reading in the paid to date as a macro variable for use later.
Next I obtain the development factors. I have set this to be the volume 12 weighted development factors but this can be changed by altering the weight macro variable.
I then apply the development factors to complete the loss triangle and I collapse these back into the incremental triangle.
So I have a completed triangle of the incremental losses. I am going to use this triangle to parameterise an over dispersed Poisson distribution for the incremental losses in each development month. An over dispersed Poisson distribution is like a Poisson distribution but the variance is greater than the mean. The ratio of the variance to the mean is known as the scale parameter. The below code creates a dataset called Loss_Statistics. For each development month this holds the average loss, the standard deviation, the variance, the scale parameter and the ODP parameters. These ODP parameters are the same as the parameters P and K for a negative binomial distribution because of the relationship between the negative binomial and the Poisson.
In this next step I am going to simulate realizations of the ultimate losses using these parameters. By using these parameters the mean of realizations will be the same as the estimate of the ultimate loss using the volume 12 method.
Finally I obtain the frequency distribution of the reserves.
SAS is very quick at running tasks like this. I simulated one million realizations in about 15 minutes. My example run output the below frequency distribution of the reserves.
Next week I will post a way of using SAS for the Bornhuetter Ferguson (BF) method. Thank you for reading and if you like this article please remember to hit the like button.