I ended up just using elastic net GLMs and weighting together an all-coverage GLM with by-coverage GLMs for all coverages, it ended up being about 50/50 for each one except Max which just used the all-coverage model. Some important features that I engineered:
(To create these features on year 5 data I saved the training set within the model object and appended it within the predict function , then deleted the training observations after the features were made. )
When you group by policy id, if the number of unique pol pay freq is > 1 it correlates with loss potential.
These people had some instability in their financial situation that seems correlated with loss potential.
When you group by policy id, if the number of unique town surface area > 1 it also correlates with loss potential.
My reasoning for this was that if someone switched the town they live in then they’d be at greater risk due to being less familiar with the area they are driving in.
I used pol_no_claims_discount like this to create an indicator for losses in the past 2 years:
x_clean = x_clean %>% arrange(id_policy,year)
if(num_years > 2){
for(i in 3:num_years){
df = x_clean[x_clean$year == i | x_clean$year == i - 2,]
df = df %>% group_by(id_policy) %>% mutate(first_pd = first(pol_no_claims_discount),
last_pd = last(pol_no_claims_discount)) %>% mutate(diff2 = last_pd - first_pd)
x_clean[x_clean$year == i,]$diff2 = df[df$year == i,]$diff2
}
}
x_clean$ind2 = x_clean$diff2 > 0, then ind2 goes into GLM.
In practice, we know that geography correlates strongly with socioeconomic factors like credit score which indicate loss potential, so I thought the best way to deal with this was to treat town surface area as categorical and assume that there are not very many unique towns with the same surface area. I don’t think this is fully true since some towns had really different population counts, but overall it seemed to work and I couldn’t group by town surface area and population because population changes over time for a given town surface area. So:
I treated town surface area as categorical and created clusters with similar frequences which had enough credibility to be stable across folds and also across an out-of-time sample.
Since Max was composed of many claim types, I created clusters based on severity by town surface area, the idea being that some areas would have more theft, some would have more windshield damage, etc.
I created clusters of vh_make_model and also of town_surface_area based on the residuals of my initial modeling. I also tried using generalized linear mixed models but no luck with that.
Two-step modeling like this with residuals is common in practice and is recommended for territorial modeling.
Since pol_no_claims_discount has a floor at 0, an indicator for pol_no_claims_discount == 0 is very good since the nature of that value is distinct. Also, this indicator interacted with drv_age1 is very good, my reasoning being that younger people who have a value of 0 have never been in a crash at all in their lives, and that this is more meaningful than an older person who may have been in one but had enough time for it to go down. This variable was really satisfying because my reasoning perfectly aligned with my fitting plot when I made it.
Other than these features I have listed, I fit a few variables using splines while viewing predicted vs. actual plots and modeled each gender separately for age. I modeled the interaction mentioned above using a spline to capture the favorable lower ages,
The weirdest feature I made that worked although wasn’t too strong was made like this:
By town surface area, create a dummy variable for each vh_make_model and get the average value of each one, then use PCA on these ~4000 columns to reduce the dimension. The idea behind this is that it captures the composition of vehicles by area which may tell you something about the region.
Another weird one that I ended up using was whether or not a risk owned the most popular vehicle for the area.
x_clean = x_clean %>% group_by(town_surface_area) %>% mutate(most_popular_vehicle = names(which.max(table(vh_make_model)))) %>% mutate(has_most_popular = vh_make_model == most_popular_vehicle)
I used 5-fold cross validation and also did out-of-time validation using years <=3 to predict year 4 and using years <= 2 to predict years 3 and 4.
For my pricing I made some underwriting rules like:
I do not insure Quarterly (meaning I multiply their premium by 10), AllTrips, risks who have a male secondary drive for coverages Max or Med 2, anyone who switched towns or payment plans ( even if one of them wasn’t quarterly), I made a large loss model for over 10k and anyone in the top 1% probability isn’t insured, and anyone with certain vh_make_models which had a really high percentage of excess claims, or people in certain towns that had really high % of excess claims. These last two were a bit judgemental because some of the groups clearly lacked the credibility to say they have high excess potential, but I didn’t want to take the chance.
I didn’t try to skim the cream on any high risk segment, but it is reasonable that an insurer could charge these risks appropriately and make a profit while competing for them. Did any of you try and compete for all trips or Quarterly with a really high risk load?
Finally I varied my profit loading by coverage and went with this in the end:
Max - 1.55
Min - 1.45
Med1 - 1.4
Med2 - 1.45
Good luck to all!
