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IAI Actuarial Core Principles · Business Economics · Pricing strategies in the financial services sector

A term insurer has two equal-sized groups of applicants it cannot tell apart. Low-risk applicants have an expected claim of ₹2,000 a year and high-risk applicants ₹6,000. Ignoring expenses and profit, the insurer charges the pooled break-even premium. Low-risk people will buy only if the premium is at most ₹3,000. What happens?

Only high-risk applicants end up buying, and the premium rises to ₹6,000. The initial pooled break-even premium is ₹4,000, which exceeds the ₹3,000 low-risk applicants will pay, so they leave and the pool's average claim becomes ₹6,000.

  1. ABoth groups buy and the insurer breaks even at ₹4,000
  2. BOnly high-risk buy; the premium must rise to ₹6,000 to break evenCorrect
  3. COnly low-risk buy; the premium falls to ₹2,000
  4. DNeither group buys because the premium is above ₹6,000
  5. Both groups buy and the insurer makes a profit of ₹1,000 per policy

Explanation

The pooled premium with both groups is (2,000+6,000)/2 = ₹4,000, above the low-risk limit of ₹3,000, so low-risk applicants leave. The pool is then all high-risk with expected claim ₹6,000, so break-even is ₹6,000. Option A ignores the exit of low-risk buyers.

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