Final answer:
An insurance company from Europe permitted to transact insurance in a specific U.S. state is known as a foreign insurer, different from domestic, excess and surplus lines, and captive insurers.
Step-by-step explanation:
An insurance company that has its principal legal address in Europe but is permitted to do business in a particular state in the United States would be classified as a foreign insurer. This classification is used to distinguish an insurance provider that is chartered (incorporated) in another country but legally allowed to sell insurance products within the state. This is in contrast to a domestic insurer, which would be an insurance company that is incorporated within the state it operates. Excess and surplus lines insurers deal with risks not covered by the standard insurance market, and captive insurers are subsidiaries created by companies to finance their own risk and insulate themselves from the traditional insurance market.