sense and nonsense of smoothing methods

When we use monte carlo simulations for practical work, then the result of the analysis is a (huge) set of samples. This is a good and pragmatic way to go and we get the respecting measures e.g. VaR, mean StDev, etc. in a robust and stable way, if we have selected a number, which is big enough for convergence of Monte Carlo (which is quite slow).

However, to work with the data in another context, e.g. as an input for another model or simply for presentation purposes, we need a smoothing method.

The easiest way is to use a parametric approach. For example find the best fitting lognormal distribution. Obviously this method is not sufficient for insurance business as the aggregated distributions can be significantly different from preselected parametric density functions.

The next level of smoothing procedures are smoothing splines kernel density estimators (check: http://en.wikipedia.org/wiki/Kernel_density_estimation). The Idea is to find a function from a sufficiently smooth family (e.g. in the L2-Space, check: http://en.wikipedia.org/wiki/Lp_space) which is close enogh to the set of samples. Here is now the major challenge to find a metric, which is good enough for insurance (especially in the tails) and still practicable.

In the current Version of P1RAT, we have an implementation of a gauss kernel and this delivers quite smooth functions. This Kernel is optimal from a ||.||2^2 norm.

What should we impement next?  I think it would be worth to think about the metric first. I thought we could minimise the kolmogrov metric or kuiper metric.

Any Ideas?