What is the legal term for one insurance company suing another to recover costs from a claim?

The correct answer is subrogation. This term refers specifically to the legal process through which an insurance company seeks to recover the amount it has paid to an insured after a loss, by pursuing a claim against a third party responsible for the loss or, in some cases, against another insurance company that may be liable.

Subrogation is important because it allows insurers to recoup costs and helps to keep insurance premiums manageable by reducing the overall cost of claims. In the context of auto insurance, for example, if one driver's insurer pays for damages after an accident, that insurer may then subrogate and recover those costs by taking legal action against the other driver's insurer if the other driver is deemed at fault.

Litigation, while related, is a broader term that encompasses any legal action taken in court and does not specifically refer to the recovery of costs between insurance companies. Mediation is a method of resolving disputes outside of court with the help of a neutral third party, which again is different from the direct legal claims made through subrogation. Negligence pertains to a failure to take reasonable care which results in harm, but does not relate to the process of one insurance company recovering costs from another.