LR Chart
Hi,
Would you please elaborate on this statement on the BattleWiki - "However, if when we plot the actual loss ratio for each quantile, the chart consists of bars increasing from left to right, then the new model is outperforming the current model."
- How is the new model outperforming?
- Do you have an example of a LR chart where new model outperform?
- What would the LR chart look like if a new model is underperforming or not performing well?
Thanks!
Comments
The premium used throughout the production of a loss ratio chart is the same, the current plan premium for a risk. We sort the risks in order of increasing predicted loss ratio as defined by new model loss cost / premium. We then compute actual loss / premium.
The new model outperforms the current plan because it groups the risks together better based on their actual loss cost. That is, it makes predictions that are closer to the actual loss cost, so when ordered by increasing predicted loss ratio the actual loss in each quantile (tends to) increase as you go from left to right. Since the premium is the same for the actual loss ratio calculation and the predicted loss ratio, this means the actual loss ratios increase. The new model will charge higher premiums as you move through the deciles from left to right and this means the actual loss ratios under the proposed plan will shift to being closer to uniform - i.e. the rating plan is more equitable as every risk has (close to) the same loss ratio.
In other words, the new model has been able to segment the risks into those that are being overcharged (low actual LR) and those being undercharged (high actual LR). The proposed premiums then bring the future loss ratios closer to being equal across all risks.
For 2 and 3, take a look at the problems posted here:
https://battleacts8.ca/8/wiki/index.php?title=Goldburd.Validation#Loss_Ratio_Charts