Fair Premiums, Insurability of Risk and Contractual
Provisions
 Fair Insurance Premiums
 What limit the insurability of risk
 Contractual provisions
 Legal Doctrines
Ins301 Ch 8&10
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Insurance Costs and Fair Premiums
 Fair premium

The premium level that is just sufficient to fund the
insurer’s expected costs and provide insurance
company owners with a fair return on their
investment. It includes



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Expected claim costs
Investment income
Administrative costs
Fair profit loading
Ins301 Ch 8&10
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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
Ins301 Ch 8&10
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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?
Ins301 Ch 8&10
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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?
Ins301 Ch 8&10
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Moral Hazard
 If you purchase a full-coverage theft insurance,
will you still take precautions to reduce the
likelihood of theft?
Ins301 Ch 8&10
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Conditions for Moral Hazard

Two conditions cause moral hazard


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Expected losses depend on insured’s behavior
Effect of behavior on expected losses is costly to
observe and measure
Example:

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Claim costs increase with driving speed
Costly for insurers to monitor driving speed
Ins301 Ch 8&10
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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?
Ins301 Ch 8&10
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Factors Limiting the Insurability of Risk
Ins301 Ch 8&10
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Deductibles

Example:

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policy with a $500 deductible
then policyholder pays first $500 of losses
Types of deductibles


per occurrence
aggregate
Ins301 Ch 8&10
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Deductibles and Claim Processing Costs


Deductibles reduce cost of processing small claims
Example:

Fixed claim processing cost of $200
Loss =
$2000
100
0
with probability 0.01
with probability 0.10
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 _______
Ins301 Ch 8&10
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Deductibles, Moral Hazard, and Adverse
Selection


Deductibles reduce moral hazard why?
Deductibles might be used to reduce adverse
selection. How?
Ins301 Ch 8&10
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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
Ins301 Ch 8&10
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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

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Reduce classification costs when consumers have information
that is costly for insurers to obtain
Example:

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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
policyholder’s jewelry
Ins301 Ch 8&10
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Pro Rata and Excess Coverage Clauses

Issue: How is coverage divided when multiple
policies apply to the same loss


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Pro rata clause: divide in proportion to amount of
coverage
Excess clause: one policy pays losses in excess of the
other policy’s 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?
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reduce administrative costs
reduce capital costs
reduce moral hazard
reduce adverse selection
Ins301 Ch 8&10
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Indemnity versus Valued Contracts

Indemnity contract - insurer pays based on the
amount of loss that occurred

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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: 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)
Ins301 Ch 8&10
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Insurance-to-Value in Property Insurance



Also called coinsurance
Specifies the percentage of the property’s value that
must be insured to receive full reimbursement in
the event of a loss
Typical coinsurance percentage is 80%
Ins301 Ch 8&10
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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
Ins301 Ch 8&10
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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.
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