Build a better Bootstrap: Distributions for the Mack method, related methods and PTF models

The Mack method has become popular as a way of computing standard deviations for volume weighted average link ratios. With the increasing prudential and regulatory need to compute other risk measures such as VaR and T-VaR actuaries have sought access to the complete probability distribution of reserves. To this end one proposed methodology in common use is the statistical Bootstrap.

Here we take a different tack and use the Bootstrap as a way of assessing the worth of any model, including the Mack method, in relation to the original data.

In this talk the Bootstrap technique is first explained in detail. At the heart of the method is a way of using any model to create many alternative datasets (called Bootstrap pseudo datasets) which reproduce key features of the original data.

We compare Bootstrap samples derived from the Mack method with Bootstrap samples based on the optimal PTF model using several real datasets. We find that Bootstrap samples (pseudo data) based on the Mack method (and related methods) do not reflect features in the original data, that is, you can easily distinguish between the real data and the Bootstrap samples. However, you cannot distinguish between Bootstrap samples based on the optimal PTF model and the original data.

The worth of the results derived from Bootstrap technique is directly dependent on the validity of the model for the data.

The powerpoint presentation is available pdf here. (1.11 MB)

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