An insurance company writing business in a state other than the one in which it is domiciled is called

A domestic insurer is one that is incorporated and operates within the same state. This term refers specifically to companies that do not extend their operations beyond state lines, thereby contrasting with foreign insurers that conduct business in states other than where they are domiciled.

An alien insurer is defined as an insurance company that is incorporated in a country outside the United States but conducts business within the U.S. This term applies to international companies and does not pertain to insurers operating between different states within the U.S., making it an inaccurate choice for the question.

A captive insurer is a type of insurance company that is created and owned by a parent company to insure its own risks. This structure is utilized for risk management purposes, and it is not defined by the geographical distinctions of operating in different states, thus making it irrelevant to the question about insurers operating outside their domiciled state.