CAS Exam 5 Fall 2014, Question 9
Study guide: Exam 5
An insurance market with a fixed number of insureds consists of two insurers — Company A and Company B. Company A has identified a new potential rating variable to segment its risks, consisting of High Risk and Low Risk.
| Variable | True Expected Cost | Insured Risks: Company A | Insured Risks: Company B |
|---|---|---|---|
| High Risk | $200 | 10,000 | 90,000 |
| Low Risk | $100 | 10,000 | 90,000 |
- All policies are annual.
- True expected cost is known only to Company A
- The probability each risk will switch insurers at renewal if they are offered a lower price by the new insurer is given by the following equation: Probability = 0.9 × (Difference in Offered Rates) / True Expected Cost
- The probability each risk will switch insurers at renewal if they are offered a higher or equal price by the new insurer is 0.
Company A intends to charge the true cost for High Risk insureds, and is evaluating two different prices for Low Risk insureds: 130 or 140. Company B charges $150 for all risks.
Part a (1.75 points)
Determine which of the two rates Company A should charge the Low Risk insureds to maximize profits, assuming Company B does not adjust its price.
Part b (0.5 points)
Describe the ultimate impact on the distribution of risks and each company's profitability if Company B does not adjust its strategy.
Part c (0.5 points)
Briefly describe two possible strategies Company B could utilize in response to Company A's new rate plan.
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