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 = ( ) 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 = ,100/1.08 = ,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 = ( ) 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, $374
Percentage loading % %
(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)