Many people ask if it is better to file the claim or pay for the damages. In general, we recommend that you file the claim. There are many benefits when you file an insurance claim that may not be obvious at the time of accident.

In your situation, the insurance company may aggressively go after the responsible party to subrogate the claim.

Recently, I had a similar situation where a driver hit our tire and left the scene. We contemplated filing the claim. I filed the claim and found out the total damage was $4800 because of damage to the steering column. While it is a different situation, it shows that it is sometimes smart to file it and let the insurance company protect you. That is why you (should) buy insurance.

It is usually better to file it with your insurance company if the amount of claim is significantly more than your deductible. "Significant" is a relative term for each person's situation. 

Good luck and let us know how you proceed.