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Risk Management and Insurance: Perspectives in a Global Economy
19. The Economic Foundations of
Insurance
There are two sections (Insurance Legal Principles; Insurance Contract Structure).
Both are derived from Appendix Chapter 2.
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Study Points
 Expected utility and the demand for insurance
 Insurance supply: characteristics of ideal insurable
exposures
3
Expected Utility and the Demand for Insurance
4
Recall the Cases
 John and Mary
• Risk-averse utility function
 XYZ Insurance
• Expected value theory
• Premium at cost
5
How Premium Is Calculated?
 Cost  expected loss
 Loadings for
• Internal expenses (e.g.,
underwriting and marketing)
• External fees (e.g., premium
taxes and license fees)
 Profits
6
Moral Hazard
 The propensity of individuals to
alter their behavior when risk is
transferred to a third party, such
as being less careful in:
• Maintaining health condition
• Driving
• House maintenance
 Fraud as an extreme case
7
Insurance Demand in Markets with Moral Hazard
 Ex-ante moral hazard
• Insurance fraud
Discussion in page 482
 Ex-post moral hazard
 Insurer responses to moral hazard
• Controlling the marginal benefit of being careful or the marginal cost
of being careless
• Loss sharing through deductible and coinsurance
• Insight 19.2
• Rewarding insureds who undertake loss preventing activities
• Retrospective or experience rating
8
Moral Hazard and Insurance Demand
Andrew
 Andrew, risk-averse salesperson
• Has €12,000 in cash and a car worth €4,000
• Probability of accident depending on his driving behavior
• If not careful, p = 0.5
• If careful, p = 0.2 but incurs additional expense of €1,000
• Has a square root function for his wealth utility
9
Moral Hazard and Insurance Demand
Ecu Insurance
 Ecu Insurance Company
• Full insurance at the actuarially fair premium
• Should it consider Andrew is a safe or risky driver?
• If a safe driver: premium = 0.2 x €4,000 = €800
• Otherwise: premium = 0.5 x €4,000 = €2,000
10
Insurer Responses to Moral Hazard
 Controlling the marginal benefit of being careful or the
marginal cost of being careless
 Loss sharing through deductible and coinsurance
• Insight 19.2
 Rewarding insureds who undertake loss preventing
activities
• Retrospective or experience rating
11
Deductible and Coinsurance (Insight 19.2)
Deductible
Insurer’s Share
Coinsurance
Coinsurance
Stop loss
Deductible
Insured’s Share
12
Deductible and Coinsurance (Another Look)
Frequency
Amount Financed
Coinsurance
Amount Retained
Stop Loss
Severity
Deductible
Coverage Limit
13
Insurance Demand in Markets with Adverse Selection
 The effect of adverse selection on insurance markets
 Insurer responses
• Eliciting more information about applicants and insureds
• Designing insurance contracts that encourage insureds with differing
risk types to self-select into the most appropriate risk class
• Table 19.1
Discussion in page 485-486
14
Adverse Selection and Insurance Demand
Individual Rating
 Two Japanese
•
•
•
•
Risk averse and each with initial wealth of ¥125,000
Will suffer a ¥100,000 loss if cancer develops
One is “low risk” (p = 0.25) and the other is “high risk” (p = 0.75)
Insurance at actuarially fair premium
15
Adverse Selection and Insurance Demand
Pooled Rating
 If the insurer pools both risks
• Fair pooled premium [(¥75,000 + ¥25,000) ÷ 2] = ¥50,000
16
A Solution
 Eliciting more information about applicants and insureds
 Designing insurance contracts that encourage insureds with
differing risk types to self-select into the most appropriate
risk class
17
An Example Using a Simple Pricing Technique
18
Insurer’s Tool – Underwriting
 Case
• A city with one health insurer, Monopoly Insurance
• All citizens must purchase health insurance.
• There are 1,000 good risk citizens and 1,000 bad risk citizens.
 Will the insurer classify them into high and low risk classes
and charge different premiums?
• No. Instead, it can treat all risks equal and charge the same
premium.
• No medical exam would be required.
19
Insurer’s Tool – Underwriting
 Suppose
• A good risk costs the insurer $1000 a year.
• A bad risk costs the insurer $5,000 a year.
 The pooled premium is then:
20
Insurer’s Tool – Underwriting
 Suppose now
• Competition Insurance enters the market.
• It has the risk information of the city.
• It wants to generate profits with minimum effort. Possible?
Medical Exam Required
Those Who Pass Gets the Coverage for $2,000 of yearly premium.
Those Who Fail Gets the Coverage for $4,000 of yearly premium.
 The result
• Monopoly Insurance goes out of business.
21
Substitutes for Insurance
 Substitutes
• Higher insurance prices tend to decrease the amount of market
insurance purchased by risk-averse individuals and increase the
amount of loss reduction “bought.”
 Complements
• Loss prevention and market insurance are complements, not
substitutes.
• An investment in loss prevention may actually raise the amount
of risk that a risk-averse person faces and therefore raises the
demand for market insurance.
22
Why Corporations Purchase Insurance
23
Why Corporations Purchase Insurance
 Already covered are:
•
•
•
•
Managerial self-interest
Corporate taxation
Cost of financial distress
Capital market imperfections
Discussion continues from Chapter 2
 Other reasons include:
• Insurers may offer real service efficiencies.
• Regulated industries have a higher demand for insurance.
• The purchase of some types of insurance is required by government.
24
“Ideal” Insurable Exposures
– Not Necessarily Practical in Some Aspects
25
“Ideal” Insurable Exposures
1. Presence of numerous independent and identically
distributed (IID) units
2. Unintentional losses
3. Easily determinable losses as to time, amount, and type
4. Economically feasible premium
26
Numerous IID Exposure Units
 Each exposure unit (e.g., liability risk) in an insurance pool
should be IID.
 Two random variables (e.g., exposures units) are
independent if the occurrence of an event affecting one of
the variables has no affect on the other variable.
• The independence property is important because it affects how well
insurers can diversify the systematic risk of their insurance pools.
 Random variables are identically distributed if the probability
distributions of two random variables prescribe the same
probability to each potential occurrence.
27
Numerous IID Exposure Units
 The law of large numbers
• Variance and standard deviation as measures of dispersion
 Effects of pooling IID exposures units – A fire insurer would
be interested in the following four statistics:
• The total amount of losses expected to be paid during the year;
• The standard deviation of the total loss distribution (to understand
the riskiness inherent in providing this insurance)
• The average loss (to determine the premium to be charged);
• The standard deviation of the average loss distribution (to determine
the risk each exposure unit contributes to the risk class)
28
Average Loss Distribution of an Insurance Pool (Figure
19.2)
29
Probability of Ruin (Figure 19.3)
30
Accidental Losses
 Losses should be accidental or unintentional
• We made this point earlier in the context of moral hazard
• From a societal viewpoint, it clearly is not good public policy to allow
policyholders to collect insurance proceeds for internationally
causing losses.
 Some losses occur naturally over time.
• It is usually less expensive to budget for possible repair or
replacement of the property than to purchase insurance.
31
Determinable Losses
 The details of the insured loss – time, place, and amount –
must be verified and the payment amount agreed upon by
the insured and the insurer.
 The costs of verifying loss details should be relatively low for
insurance to be offered at an economically feasible
premium.
32
Economically Feasible Premiums
 On the one hand, rational risk-averse individuals will pay a
maximum premium equal to the expected value of the loss
plus the risk premium. On the other, the owners of private
insurance companies require that insurance rates be
enough to give them a competitive return on their
investments.
 Factors affecting this range
•
•
•
•
•
•
Competition in the market
Threats of new entrances
Price
Threat of alternative products and substitutes
The bargaining power of consumers
The degrees of risk attitudes of consumers
33
Legal Aspects: A Short Visit
Appendix Chapter A2
34
Legal Principles
1. Indemnity
2. Insurable interest
3. Utmost good faith
35
Indemnity
 In nonlife insurance
• Actual cash value (ACV)
• Replacement cost
• Valued policy
• Other insurance provision
• Primary and excess
insurance
 Figure A2-1
• Subrogation
36
Another Example of Primary and Excess
Personal Umbrella Liability Insurance
(Liability Coverage)
Excess
$1,000,000
Homeowner’s
(Liability Coverage)
$500,000
Personal Automobile
(Liability Coverage)
Primary
$300,000
37
Indemnity
 In life insurance
• No application of “other insurance” provision
• When applied, it could be in relation to the total earnings power
of the insured life and the sum of life insurance in the aggregate
of all outstanding policies
• Thus, life insurance policies are “valued policies.”
 In health insurance
• ‘Coordination of benefits”
38
Insurable Interest
 The principle:
• An insured must have a financial
interest in the loss event that is the
subject of the insurance contract
for the policy.
 Application in
• Nonlife insurance
• Bailment
Bailment – Temporary change in
possession of property but with
no change in ownership
• Life insurance
• Insurable interest for domestic
partners  Insight A2-2
• Viatical Settlements (and
Death Bonds)  Insight A2-3
39
Utmost Good Faith
 A higher degree of honesty on
the parties to an insurance
contract than what is expected
from parties to other [legal]
contracts
 Information asymmetry problem
inherent with insurance contracts
http://www.lawyersrealestate.com.au/blogger/2006_04_01_archive.asp; http://www.freerepublic.com/focus/f-news/1780026/posts
40
Utmost Good Faith – Applications
 Misrepresentation
• Material response incorrectly made by an applicant in procuring
insurance
 Concealment
• Intentional failure to disclose material information
 Warranty
• Statement of fact or promise that must be true for the insurer to be
liable under the insurance contract
41
42
Insurance Contract: A Short Visit
Appendix Chapter A2
43
Characteristics
 Aleatory contract
• The values exchanged by the contracting parties may not seem
equal.
•
 Unilateral contract
• Only one party (the insurer) has a legal duty to act.
 Conditional contract
• The insurer is obligated to honor its promises only if the insured has
complied with certain conditions specified in the policy.
44
Characteristics (continued)
 Personal contract
• The agreement is between the insurer and the insured person (not
the insured property).
• Hence, property insurance contracts cannot be assigned to
another insured person without the insurer’s consent.
 Contract of adhesion
• The contract is designed by one party and offered to another party
on a "take it or leave it" basis.
 Reasonable expectations doctrine
• It considers the objectively reasonable expectations of insureds and
beneficiaries regarding the terms of insurance contracts.
45
The Insurance Contracting Process
 Offer and acceptance
• Binding authority
• Conditional premium receipt
 Consideration
• Insurer – promise to pay the stipulated insurance benefits
• Insured – complete application and initial premium payment
 Legal competence
• Age?
 Legal purpose
46
Structure of the Insurance Contract
1. Declarations
2. Insuring agreements
3. Exclusions
4. Conditions
5. Endorsements (riders)
47
Declarations (Page)
 Policy limits
• Aggregate limits
• Sublimits such as:
• Per person limit
• Per occurrence limit
Insight A2-4
Automobile Liability Insurance Limits
 Loss sharing
• Deductible
• Elimination period (e.g., health insurance)
• Coinsurance
48
49
Insuring Agreements
 Describes the nature of the insurer's obligations:
• Promises to pay certain sums upon the occurrence of enumerated
events, for example:
• Property damage to covered property caused by insured perils
• Payment for settlements and judgments when the insured is
found legally liable for activities covered in the contract
• Plus a duty to defend the insured against all allegations
• Life insurer’s promise to pay the beneficiary (or insured) certain
amounts upon the death (or survival) of the insured
• In health insurance, reimbursement of covered medical expenses
or the periodic payment of income for covered disabilities
50
Exclusions
 A necessary element of the contract for the following
reasons
• Insurable risks should be independent and identically distributed loss
events.
• Problems of moral hazard must be addressed.
• When applicable, the insurer avoids overlapping coverage and the
inefficiency created by such redundancy.
• Exclusions can serve to limit coverage to make the premium more
affordable.
51
Conditions
 The insured must meet these conditions to keep the policy
valid and to receive applicable benefits.
• Prompt notification of a loss event
• Mitigation of the property from further loss
• Documentation of evidence
• Cooperation to the insurer and investigation
52
Conditions – Termination of Contract
 Cancellation
Cancellation differs from voiding (avoiding)
a contract or void contract.
 Nonrenewal
53
Endorsements and Riders
 Added to the standardized contract to modify the terms and
conditions of the policy.
• Endorsements commonly used in nonlife insurance business
• Riders commonly in life insurance business
54
Discussion Questions
55
Discussion Question 1
 Hannah owns a home
worth US$50,000, which is
subject to the risk of fire.
The probability of a fire is
25 percent and the amount
of damage due to the fire
would be US$40,000.
Assume Hannah’s utility
function is the square root
of wealth. Hannah has
been offered full insurance
at a cost of US$13,000. Will
she buy the insurance?
Why or why not?
56
Discussion Question 2
 A frequency distribution shows the number of accidents that
an insurer can expect from each exposure unit in its
insurance pool during the year. Use the information provided
below to answer the following questions:
• Calculate the expected number of accidents a single exposure unit
could expect during the next year.
• Calculate the standard deviation of the number of accidents a single
exposure unit could expect during the next year.
• Calculate the standard deviation of the number of accidents.
57
Discussion Question 3
 Consider the following lotteries, x, y and z:
• Calculate the expected value of each gamble.
• Assuming a risk-averter’s utility function of wealth is given below.
Calculate the expected utility of each gamble for a person who has
an initial wealth level of 10. Which gamble does this person prefer?
Why?
58