Fair Premiums, Insurability of Risk and Contractual Provisions

1
Fair Premiums, Insurability of Risk and
Contractual Provisions

• Fair Insurance Premiums
• What limit the insurability of risk
• Contractual provisions
• Legal Doctrines

2
Insurance Costs and Fair Premiums

• Fair premium
• The premium level that is just sufficient to fund
  the insurers expected costs and provide
  insurance company owners with a fair return on
  their investment. It includes
• Expected claim costs
• Investment income
• Administrative costs
• Fair profit loading

3
Claim tail and present value

• The lag between the time that coverage is sold
  and claims are paid is known as the claim tail.
• It affects expected losses

4
Example

• Suppose a liability claim longs for 3 years. In
  the first year, the loss amount on average is
  700. In the second year, the loss amount is
  200. the loss amount is 100 in the third year.
  Interest rate is 5. What is the expected loss?

5
Premium loadings

• Two Bicycles one worth 200 and the other worth
  6000. Assume that the probability of each bike
  being stolen is 0.05. Assume that the fixed costs
  of paying employees to market, underwrite, and
  process an application for bike insurance are
  100 and that capital costs are 0. ignoring
  investment income, what are the fair premiums for
  both?

6
Moral Hazard

• If you purchase a full-coverage theft insurance,
  will you still take precautions to reduce the
  likelihood of theft?

7
Conditions for Moral Hazard

• Two conditions cause moral hazard
• Expected losses depend on insureds behavior
• Effect of behavior on expected losses is costly
  to observe and measure
• Example
• Claim costs increase with driving speed
• Costly for insurers to monitor driving speed

8
Adverse Selection

• If insurer is unable to distinguish between the
  two types of consumers with different risk level
  and thus change them the same premium, what will
  happen?

9
Factors Limiting the Insurability of Risk
10
Deductibles

• Example
• policy with a 500 deductible
• then policyholder pays first 500 of losses
• Types of deductibles
• per occurrence
• aggregate

11
Deductibles and Claim Processing Costs

• Deductibles reduce cost of processing small
  claims
• Example
• Fixed claim processing cost of 200
• 2000 with probability 0.01
• Loss 100 with probability 0.10
• 0 with probability 0.89
• Expected claim cost w/o a deductible ______
• Expected claim cost w a 100 deductible ______
• Marginal cost of insuring the 100 loss equals
  _______

12
Deductibles, Moral Hazard, and Adverse Selection

• Deductibles reduce moral hazard why?
• Deductibles might be used to reduce adverse
  selection. How?

13
Coinsurance

• With coinsurance, insured pays a proportion (the
  coinsurance rate) of any loss
• Example Insured pays 20 of all medical costs
• Reason for coinsurance provisions
• Insureds demand less than full insurance when the
  policy has a loading
• Reduce moral hazard

14
Policy Limits

• A policy limit is the maximum amount that the
  insurer will pay
• Liability insurance always has a policy limit
• Property insurance often has a policy limit

15
Purpose of Policy Limits

• Reduce classification costs when consumers have
  information that is costly for insurers to obtain
• Example
• Homeowners policy might limit coverage for
  jewelry losses to 2,500
• Those with more expensive jewelry buy special
  coverage
• Insurer does not have to investigate the value of
  each policyholders jewelry

16
Pro Rata and Excess Coverage Clauses

• Issue How is coverage divided when multiple
  policies apply to the same loss
• Pro rata clause divide in proportion to amount
  of coverage
• Excess clause one policy pays losses in excess
  of the other policys limit
• Why have these clauses?
• prevent coverage in excess of loss, which would
  cause moral hazard

17
Exclusions

• Policies exclude coverage for some types of
  losses
• Why?
• reduce administrative costs
• reduce capital costs
• reduce moral hazard
• reduce adverse selection

18
Indemnity versus Valued Contracts

• Indemnity contract - insurer pays based on the
  amount of loss that occurred
• Example auto physical damage
• Valued contract - insurer pays a pre-determined
  amount
• Example life insurance

19
Indemnity versus Valued Contracts

• Type of contract is largely explained by
• The costs of assessing value when the amount of
  loss can be assessed at low cost following the
  loss, more likely to have indemnity contracts
• Moral hazard when moral hazard is less likely to
  be a problem, fixing the insurance payment before
  a loss can avoid costly haggling following a loss
  (e.g., life insurance)

20
Insurance-to-Value in Property Insurance

• Also called coinsurance
• Specifies the percentage of the propertys value
  that must be insured to receive full
  reimbursement in the event of a loss
• Typical coinsurance percentage is 80

21
Legal Doctrines

• Indemnity principle an insurance policy cannot
  pay more than the financial loss suffered.
• Insurable interest if you want to get paid from
  insurance company, you got to have interest.
• Example, A and B are not related, A buys a life
  insurance and set B as the beneficiary
• Subrogation after a party receives claim payment
  from an insurer, it has to transfer the right to
  seek additional compensation to the insurer

22
Legal Doctrines

• Utmost good faith
• Misrepresentation (page 195)
• Concealment (196)
• Contract of adhesion
• Favors insureds, if disagreement
• Doctrine of reasonable expectation
• Policies would be interpreted based on the
  expectation of a person who is trained in the
  law.