Chapter Outline

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Chapter Outline

• 8.1 FACTORS THAT LIMIT THE INSURABILITY OF RISK
• Premium Loadings
• Exposures with Low Severity
• Exposures with High Frequency
• Correlated Exposures
• Exposures with Parameter Uncertainty
  (Uncertain Expected Losses)
• Moral Hazard
• Conditions for Moral Hazard
• Reducing Moral Hazard
• Moral Hazard in Other Contexts
• Adverse Selection
• Example of Adverse Selection

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Chapter Outline

• 8.2 CONTRACTUAL PROVISIONS THAT LIMIT COVERAGE
• Deductibles
• Deductibles and Claim Processing Costs
• Deductibles and Moral Hazard
• Deductibles and Adverse Selection
• Coinsurance
• Policy Limits
• Pro-Rata and Excess Coverage Clauses
• Exclusions
• Indemnity versus Valued Contracts
• Insurance-to-Value (Coinsurance) In Property
  Insurance
• 8.3 LEGAL DOCTRINES
• Reducing Contracting Costs through Fundamental
  Legal Doctrines
• Mitigating Moral Hazard
• Information Disclosure
• Resolving Coverage Disputes
• 8.4 SUMMARY

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Factors Limiting the Insurability of Risk

• Figure 8-1

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The Effect of Premium Loadings

• Higher loading gt lower demand for coverage
• Thus, factors that raise premium loadings limit
  the amount of risk that is insured
• administrative costs
• capital costs (risk load)
• Also, insurance for some types of exposures is
  likely to be extremely limited (or nonexistent)

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Exposures with Low Severity

• Fixed administrative costs gt
• Exposures with low value will not be insured on
  an individual basis
• Example
• insuring a 200 bike compared to a 6,000 bike

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Exposures with High Frequency

• High frequency gt
• Premium will be close to the potential loss
• Example
• 10,000 with probability 0.7
• Claim
• 0 with probability 0.3
• Loading 25 of expected loss
• Premium 1.25 x 7,000 8,750
• Little demand for such insurance

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Exposures with Correlated Losses

• Correlated losses gt
• Insurer needs to hold a large amount of capital
  to make promise to pay claims credible
• Therefore, profit loading is high
• Thus, less insurance coverage for highly
  correlated losses

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Exposures with Parameter Uncertainty

• Parameter uncertainty insurer does not know the
  true expected loss
• If estimate of expected loss is too low for one
  policyholder, then estimate is too low for many
  policyholders (insurers errors in predicted
  losses are correlated)
• Insurer needs to hold a large amount of capital
• Profit loading is high
• Less insurance for exposures with significant
  parameter uncertainty

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Exposures with Parameter Uncertainty

• Example
• Property valued at 50,000, lots of policyholders
• Probability of loss 0.02 or 0.04
• Insurer does not which probability is the true
  one
• Insurer view each probability as equally likely
• Insurers expected claim costs 1,500
• But insurer knows that claim costs could be much
  higher
• Insurer needs a lot of capital (more than 500
  per policyholder)

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Moral Hazard

• Moral hazard refers to the effect of insurance on
  the insureds incentives to reduce losses
• Examples
• drive less carefully when insured
• consume more health care when insured
• Main Point
• Moral hazard causes less than full insurance
  coverage
• Intuition if insurance causes moral hazard, then
  less insurance limits moral hazard

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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

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Implications of Moral Hazard

• Consumers will want contracts that reduce moral
  hazard otherwise, they must pay higher premiums
• Contracts will place some risk on the insureds
• Deductibles
• Coinsurance

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Moral Hazard in Other Contexts

• Moral hazard is a pervasive problem
• Examples
• employment contracts
• social policy
• Fundamental Tradeoff
• More insurance coverage gt Less incentive to
  avoid a loss
• Therefore, usually will have less than full
  insurance

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Adverse Selection

• Adverse selection occurs when
• policyholders have different expected losses
• insurers cannot classify
• gt same price to all
• At a given price,
• higher risk consumers will buy more coverage
• lower risk consumers will less coverage
• Thus adverse selection gt low risk people
  obtain less coverage

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Contractual Provisions that Limit Coverage

• Summary of previous slides
• Coverage is limited by administrative costs,
  capital costs, moral hazard, and adverse
  selection
• Contractual provisions that limit coverage will
  now be described
• deductibles
• coinsurance
• policy limits
• exclusions

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Deductibles

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

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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 claim processing cost w/o a
  deductible 30 22 52
• Expected claim cost claim processing cost w a
  100 deductible 19 2 21
• Marginal cost of insuring the 100 loss equals
  31

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Deductibles and Moral Hazard

• Deductibles reduce moral hazard
• insureds take greater care if they have to pay
  part of the loss

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Deductibles and Adverse Selection

• Deductibles might be used to reduce adverse
  selection
• Recall, adverse selection occurs when the insurer
  cannot classify, but the policyholders know their
  risk
• At a given price,
• high risk people will buy more coverage
• low risk will buy less coverage

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Deductibles and Adverse Selection

• Idea
• Insurer offers multiple policies with different
  deductibles and different prices per dollar of
  coverage
• Lower deductible (higher coverage) policies have
  a higher price per dollar of coverage
• Higher risk people might choose the lower
  deductible (higher priced) policies
• Lower risk people might choose the higher
  deductible (lower priced) policies
• Thus policyholders separate themselves into
  different policy groups

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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

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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

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Purpose of Policy Limits

• People have limited amount of wealth they want to
  protect
• 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

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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

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Exclusions

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

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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

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Indemnity versus Valued Contracts

• Type of contract is largely explained by
• the costs of assessing value
• moral hazard
• When the amount of loss can be assessed at low
  cost following the loss, more likely to have
  indemnity contracts
• 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)

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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

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Insurance-to-Value in Property Insurance

• Let
• C amount of coverage purchased (policy limit)
• L the amount of the loss
• V value of property at the time of the loss
• r coinsurance rate
• Insurer will pay the lesser of
• C , L ,
• Example
• C 150,000, V 200,000, r 80 gt C/Vr
  93.75
• Loss Insurer pays
• 100,000 93,750
• 150,000 140,625

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Why Have Legal Doctrines?

• Why not allow free contracting?
• Legal doctrines reduce contracting costs
• difficult to anticipate every possible
  contingency and to write very detailed contracts
• therefore it is useful to have principles that
  will be applied to unforeseen circumstances
• applicable especially to the problems of
• moral hazard
• information disclosure
• Legal system also helps resolve disputes and
  enforce contracts

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Legal Doctrines and Moral Hazard

• Mitigating Moral Hazard
• Indemnity Principle
• Insurable Interest
• Subrogation

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Legal Doctrines and Information Disclosure

• Inducing truthful information disclosure
• utmost good faith
• misrepresentations
• concealment

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Resolving Coverage Disputes

• Contracts of Adhesion
• ambiguities are interpreted in favor of
  policyholder
• applied less often to commercial insurance
• Doctrine of Reasonable Expectations
• courts interpret contracts as would a reasonable
  person not trained in the law
• Bad Faith Suits