Final answer:
A captive insurance agency solicits insurance to its members, allowing a parent company to control costs and risk management. An actuarially fair premium charged to a whole group may lead to a loss of competitive edge and potential insolvency.
Step-by-step explanation:
An organization that solicits insurance only to its members is known as a captive insurance agency. Captive insurance agencies are created by companies to underwrite their own risks. This approach can offer financial benefits because it allows the parent company to have more control over their insurance costs and risk management practices. If an insurance company tried to charge an actuarially fair premium to the group as a whole rather than to each group separately, they would likely incur losses for high-risk members while potentially overcharging low-risk members, leading to a loss of competitive edge and potential insolvency if not managed correctly.