The insurer's right to recover its claim payment to an insured from a negligent third party is known as

Arbitration refers to a method of resolving disputes outside of the courts, where an impartial third party makes a decision. It does not involve the insurer's recovery of payments made to the insured nor does it pertain to rights against third parties. Thus, arbitration does not relate to the insurer's claim recovery process.

Assignment involves the transfer of rights or benefits from one party to another, such as when an insured assigns their rights to claim benefits to a third party. While it can relate to insurance policies, it does not specifically address the insurer's right to recover from a negligent third party, which is a key aspect of subrogation.

Liberalization is a clause in insurance policies that allows the insurer to extend improved coverage to all policyholders without additional premium charges. This term does not relate to the insurer's rights against third parties for recovery of claims, and thus it is not relevant in this context.