Expected Value Insurance Claims

Question

Based on an insurance company's past data, each year an average of 1/90 policy holders make a claim of $250, 1/100 policy holders make a claim of $12,000, and 1/500 make a claim of $27,000.

7. What would the insurance company have to charge per policy-holder to break even? (i.e., what the premium would have to be in order to have an expected profit of zero.)
$ (Round to the nearest dollar.)

8. A renters insurance policy sell for $400 annually. What is the expected profit or loss for the company per policy-holder over the course of the year?
$ (Round to the nearest dollar.)

9. If the company sold 650 policies what would the overall expected profit or loss be?
$ (Round to the nearest dollar and do not use commas.)

Answer 1

Expected Value Insurance Claims

1. Expected Annual Claim Cost per Policyholder

• Claim A: (1/90) × 250 = 2.78

• Claim B: (1/100) × 12,000 = 120

• Claim C: (1/500) × 27,000 = 54

Total Expected Cost = 2.78 + 120 + 54 = 176.78 ≈ 177

2. Break-Even Premium

Required premium = Expected cost ≈ $177

3. Expected Profit on a $400 Policy

Profit = 400 – 176.78 ≈ 223

Expected profit per policyholder = $223

4. Expected Profit for 650 Policies

650 × 223.22 ≈ 144,093

Total expected profit = $144,093