By how much? Logically, the fair amount to raise rates would be the amount that compensated for their increased risk of doing it again. There you are, doing a risk analysis.
(If you had them directly pay for the damage they caused, that wouldn't be insurance, that would be a middle man for restitution.)
By some amount proportional to the damage caused, of course. The more times you cause damage, and the higher the damages, the higher your rates go over time.
I think my point is pretty clear without me coming up with a precise formula: instead of predicting rates, just adjust them based on history instead. After all, someone likely to cause repeated damage in the future is also likely to have caused it in the past.
The only major difference between the two approaches is that mine doesn't require someone to make predictions - which might be biased - in exchange for mine maybe under-charging someone with no negative history who is about to cause a huge amount of damage and then stop paying into the system (death, etc). But in those (rare?) cases, the fact that everyone is part of the system means that the single rare loss is amortized nicely and without bias.
>The more times you cause damage, and the higher the damages, the higher your rates go over time.
But by how much? If it's enough to fully offset the cost of the damage, that's not insurance, but a payment plan. If it's less than the cost of the damage, then you have to decide what it's going to be.
(If you had them directly pay for the damage they caused, that wouldn't be insurance, that would be a middle man for restitution.)