Moreover, our insurance depends on the car we drive, our past record of insurance claims and also on whether it can be shown that we were negligent or not. In other words, insurance companies worry about the behaviour that insurance induces.
The trade-off between ex ante and ex post efficiency is apparent from the fact that if the deductible is too high, it may discourage insurance and therefore driving altogether. If, on the other hand, the deductible is too low, then drivers may become imprudent again.