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Insurance pricing

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Qingyu Li

on 7 February 2013

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Transcript of Insurance pricing

Expected Claim Cost Regulations What are the determinants of insurance premiums ? Investment Income Administrative Costs How are administrative costs included in the premium? Fair Profit Loading Why insurers classify buyers into groups? Probability of loss 0.15 Probability of no loss 0.85 Loss amount $1,000 Expected Loss for one insurance buyer = 0.15*1000+0.85*0 = $150 Each buyer has the same loss distribution
Each buyer's loss is independent with the loss of other buyers Loss distribution: Distribution of average losses will concentrated around $150: Heterogeneous Buyers Group Bookworms
Skateboarders Pr(loss) Pr(no loss) Expected Loss amount $100
$200 0.9
0.8 0.1
0.2 What will happen if insurance company charge the same rate to the two groups? Produce large profits in the short run
Adverse selection in the long run Risk classification estimate expected claim cost for different buyers
charge premiums according to expected claim costs Homogeneous Buyers: Law of Large Numbers
Each loss is uncorrelated with others Insurance buyers with different loss distributions Result of risk classification: Redistribution effects Risk Classification Practices Class rate merit rating bonus-malus rating: no-claims discount system
retrospective experience rating - medium to large business
prior loss experience - individuals and small to mid-size businesses experience rating: non experience rating factors class rate
underwriting Regulation of rate changes Prior approval laws Competitive rating laws rate changes must be approved before the new rate can be used rate changes must be filed with state insurance departments
do not require approval by regulators Regulation of rating factors Incentive for risk control Fairness, imperfect classification Insurance Premium Behavioral effects Classification cost reduce cross-subsidy
redistribute wealth from high risk to low risk buyers increase the cost of risky behaviors
provide economic incentives to reduce cost of risks classify and evaluate applicants incur costs
high classification cost might increase total cost of risk
low classification cost will cause decline in total cost of risk Capital Shocks Underwriting Cycle Effect of regulating rate change temporarily reduce rate change Why regulate policyholders with different expected claim costs might be placed in the same risk class. Subjective classification factors observed at low cost: sex, age, geographic region, and credit history
whether use of these factors and other information should be prohibited?
Basic theory of competitive risk classification Residual market system force insurers to collectively supply coverage to most if not all applicants
insurer must participate in order to sell coverage in the voluntary market What happens when interest rates rise? Why does investment income affect insurance premiums? Claims Tail: The lag between the time coverage is sold and claims are paid

Claims are paid during the year of coverage or one year after
Claims are paid a number of years after coverage period Claims Tail Negatively related to
Level of interest rates
Length of claims tail

Why does investment income affect premiums?
Ability of insurer to earn income from investing premium dollars Fair Premium How much money does the insurer need to collect at the beginning of the year to pay $100 in claims?

P( 1 + r ) = 100
P = 100/(1+r)
r = 0.10 P = $90.91
r = 0.05 P = $95.24

As interest rate increases, the premium decreases Claims Paid at One Year P + rP = 100/(1+r)
= P = 100/(1+r)2

r = 0.10 P = $82.64
r = 0.05 P = $90.71

Values are lower than claims paid at one year Claims Paid at Two Years Amount of money needed to fund expected claim costs taking into consideration the insurer’s ability to earn investment income

Expected Claim Cost x Discount Factor Discounted Expected Claim Cost Included in fair premium to cover...
Underwriting expenses
Loss adjustment expenses

30-50% of premium Expense Loading The extra amount that policyholders must pay to compensate investors for providing capital
Interest Rate = 10%
Administrative = 20% of expected claim cost
Profit Loading = 5% Step 1 : Expected Claim Cost
= (0.1)($10,000) = $1,000
Step 2 : Discounted Expected Claim Cost
= $1,000/(1.1) = $909.09
Step 3 : Administrative Expenses
= (0.20)($1,000) = $200
Step 4 : The Required Profit Loading
= (0.05)($1,000) = $50
Step 5 : Fair Premium
= $909.09 + $200 + $50 = $1,159.09 Capital Shocks: Large industrywide reductions in capital caused by adverse loss or investment experience - Higher claim costs one year increase insurers estimate of expected costs for the next year Possible Effects Large Loss May increase the expected claim cost for new policies Shift back of industry supply curve Higher expected claim costs imply higher insurance premiums Underwriting Cycle: A cycle in premium and insurer operating profits Soft Markets Numerous insurers seeking to write new coverage Stable prices Hard Markets Reductions in the supply of coverage Sharp price increases Advantage or Disadvantage? Causes Capital Shock Theory Insurers charge inadequate prices What two things are included in administrative costs? Suppose you wanted to find the fair premium for a group of insurance policies each having the following loss distribution: Loss = $10,000 with probability 0.1
$ 0 with probability 0.9 Practice Problem Rate=price per unit of coverage
Total premium= rate × coverage purchased
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