Weather-Insurance Portfolio Profitability

Setup

You price a 12-month weather insurance policy. Customers pay premiums upfront for the year. Each policy can generate regulatory and servicing costs, and possibly a claim. Assume at most a small expected number of claims per policy-year (treat the "claim rate" as the expected number of claims per policy-year; if at most one claim occurs, this equals the annual claim probability).

• Premium: $30 per month, paid for 12 months upfront.
• Servicing cost: $3 per month.
• Benefit (indemnity) per claim: $8,000.
• Regulatory cost: $4 per quarter, plus$ 300 per claim.

Tasks

1. What claim rate yields breakeven on a per-policy annual basis?
2. You have four customer segments A–D with different annual claim rates (expected claims per policy-year): r_A, r_B, r_C, r_D. Which segment combination maximizes profit, and why? State the rule you would use.
3. After choosing the optimal set of segments, illustrate how adding B, C, and D changes profit compared with offering only to A. Show both a general formula (per policy and with policy counts if available) and a small numeric example to make it concrete.

Assumptions

• Costs given are per policy unless noted.
• Ignore time value of money since premiums are paid upfront and no discount rate is specified.
• Regulatory cost " $4/quarter" is per policy (so$ 16 per policy-year).