Go after the car owner's insurance, and if they won't compensate you, simply make a claim with your own insurance company.
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While I agree with Mr. Lassen, I would also look to see if the person who stole the car was arrested. If so, you may be able to file a restitution claim in the criminal case. It is a very slow way to get reimbursed, but you can be compensated for the damage and the restitution order is not discharged in bankruptcy.