pricing example 1 $100,000with prob. 0.02 loss = $20,000with prob. 0.08 0with prob. 0.90 find fair...
Post on 25-Dec-2015
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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)
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