An insurer that primarily assumes and spreads liability-related risks to its members who are engaged in a similar business activity is a

An unauthorized insurer is one that is not licensed to operate in a particular state and does not have the legal authority to provide insurance in that jurisdiction. This type of insurer does not primarily focus on pooling risks among similar businesses, but rather operates outside regulatory oversight, making it a less relevant option for the question.

Reinsurance companies provide insurance to other insurers, allowing them to transfer portions of their risk portfolios. While they do spread risk, they do not directly engage with members in a specific business activity as a risk retention group does. Their primary function is to support other insurers rather than to facilitate a collective risk-sharing arrangement among similar businesses.

A stock insurer is a type of insurance company owned by shareholders who may profit from its operations. While they provide various types of insurance coverage, they do not specifically focus on liability risks for members of similar business activities in the same way as risk retention groups, which are dedicated to mutual support for their member businesses.