Which term describes an insurance company incorporated outside the United States?

The term that describes an insurance company incorporated outside the United States is "Alien Insurer." This classification is used to identify insurers that are established in a different country. Insurance companies are categorized based on the location of their incorporation relative to the state in which they are operating.

A domestic insurer is one that is incorporated within the state it operates, while a foreign insurer is one incorporated in another state within the U.S. The term "mutual insurer" refers to a specific type of insurance company owned by its policyholders, rather than its incorporation status. Consequently, "Alien Insurer" effectively captures the essence of an insurance company formed outside the borders of the United States, making it the correct answer in the context of this question.