Final answer:
Information on how sensitive companies are to changes in actuarial assumptions can be identified by analyzing the impact of charging an actuarially fair premium to an entire group, as opposed to specific risk groups, which may lead to adverse selection and financial instability for the company.
Step-by-step explanation:
Actuarial Assumptions and Premiums
When insurance companies set premiums, they use actuarial assumptions to assess the risks associated with different groups. If an insurance company charges the actuarially fair premium to the group as a whole rather than to each group separately, they must consider the average risk across all groups. For example, in a scenario where 50-year-old men are divided into two groups based on family history of cancer with different mortality rates (1 in 50 for those with a history vs. 1 in 200 for those without), the actuarially fair premium would be different for each group. Charging the same premium to all ignores individual risk factors, which could result in adverse selection, as lower-risk individuals may choose not to purchase insurance, leaving the company with a higher-risk pool.
If the company charged the actuarially fair premium to the entire group without accounting for family cancer histories, they would need to calculate a blended rate that reflects the combined risk. However, this could cause the insurer to lose lower-risk customers who might find the premium unfairly high compared to their actual risk. In the long term, this could jeopardize the company's financial stability and compromise its ability to cover all claims adequately.