Pricing Example 1

1
Pricing Example 1

• 100,000 with prob. 0.02
• Loss 20,000 with prob. 0.08
• 0 with prob. 0.90
• Find Fair Premium if
• policy provides full coverage
• underwriting costs 20 of pure premium
• claims are paid at end of year
• interest rate 8
• claim processing costs 5,000
• fair profit 5 of pure premium

2
Pricing Example 1

• Solution
• pure premium 3,600
• PV of expected claims 3600/1.08
• underwriting costs fair profit (0.20 0.05)
  x 3,600 900
• expected claim processing costs 5,000 x 0.10
  500
• PV of expected claim processing costs 500/1.08
• Fair premium 900 4,100/1.08 900 3,796
  4,696

3
Pricing Example 2

• 100,000 with prob. 0.02
• Loss 20,000 with prob. 0.08
• 0 with prob. 0.90
• Find Fair Premium if
• policy has a 20,000 deductible
• underwriting costs 20 of pure premium
• claims are paid at end of year
• interest rate 8
• claim processing costs 5,000
• fair profit 5 of pure premium

4
Pricing Example 2

• Solution
• pure premium 0.02 x 80,000 1,600
• PV of expected claims 1600/1.08
• underwriting costs fair profit (0.20 0.05)
  x 1,600 400
• expected claim processing costs 0.02 x 5,000
  100
• PV of expected claim processing costs 100/1.08
• Fair premium 400 1,700/1.08 400 1574
  1,974

5
Comparison of the Two Examples

• Note difference in loading on the two policies
• Full coverage Deductible
• Premium 4,696 1,974
• Expected claim cost 3,600 1,600
• Dollar loading 1,096 374
• Percentage loading 30.4
  23.4
• (relative to exp. claim cost)
• Difference is due to the deductible policy
  eliminating expected claim processing cost on
  relatively frequent, low severity claims (see
  Chapter 8)