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

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

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

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

Comparison of the Two Examples

• Note difference in loading on the two policies

Full coverageDeductible

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)