Most uses of ML in reserving involve using ML techniques to get a single estimate of a loss reserve. Sometimes we may fit an ensemble of models and average over these, but the end result is still the same - a point or central estimate. There are some exceptions to this - for example, we have discussed Al Mudafer’s work used Mixed Density Networks to estimate reserve distributions.
In some recent personal research work that has overlaps with the interests of the MLRWP, Greg Taylor and I took a different approach to estimating uncertainty. We split loss reserving uncertainty into a number of different components, namely:
- Internal model error (loosely speaking, the error introduced from fitting the wrong model structure to past data)
- External model error (even if our past model is correct, the future may be very different due to systemic factors like the economic environment, legislative change etc)
- Parameter error (even if our model assumptions were correct, our parameter estimates may not be)
- Process error (even if our model were exactly correct, future outcomes are still subject to randomness)
- Model distribution error (our model structure may be right our distribution assumptions may not be).
We then looked at estimating 1, 3 and 4 from this list and took advantage of:
- Our existing approach to build self-assembling loss reserving models using the LASSO
- The Bayesian interpretation of the LASSO which allows us to calculate a posterior loss reserving distribution
- Long-accepted methods for estimating parameter and process errors using bootstrapping and Monte Carlo simulation
- A healthy dose of pragmatism based on years of loss-reserving experience.
We combined all these steps to produce an estimate of loss reserve uncertainty. Typically bootstrapped estimates of loss reserves just consider the independent errors (parameter and process, 3 and 4 on the list) so the addition of internal model error (1) makes our estimate more comprehensive. The estimate is still incomplete because it doesn’t include 5 from the list above (probably not all that big) or 2 (almost certainly significant, but requires estimation through more qualitative methods).
If you’d like to learn more about what we did then see the following resources: