# “Improving Segmentation” (using Lorenz curves, or sort of)

This afternoon, André did send me an interesting graph about the use of Lorenz curve in the context of insurance pricing (and modeling) It is some sort of Lorenz curve, upside-down, with on the x-axis the proportion of the population, and on the y-axis the proportion of the losses. The important point is that the population is sorted according the their risk, i.e. their premium. The code to generate such a curve is actually quite simple,

```L <- function(u,varx="premium",vary="losses"){
base=base[order(base[,varx],decreasing=TRUE),]
base\$cum=(1:nrow(base))/nrow(base)
return(sum(base[base\$cum<=u,vary])/
sum(base[,vary]))}

vu=seq(0,1,by=.01)
vv=Vectorize(function(u) L(u))(vu)```

My concern was more on two labels on the figure, with on the top-left “perfect pricing” and on the first diagonal “average pricing“. What could that possibly mean? Is there even such a thing as a “perfect pricing“? In order to understand what we plot here, let us generate some dataset, and fit some model. Including things that might be seen as the “perfect model“: the price base on the parameters used to generate the data, and the model used to generate the data, fitted on the data.

# Further readings on GLMs and ratemaking

Some articles found in Actuarial journal, on ratemarking,

and in the CAS forums, and Astin conference papers