Transcript Insurable Exposures

Fall 2008 Version
Professor Dan C. Jones
FINA 4355
Class Problem
Risk Management and Insurance: Perspectives in a Global Economy
19. The Economic Foundations of
Insurance
Professor Dan C. Jones
FINA 4355
Class Problem
Study Points
Expected utility and the demand for insurance
Insurance supply: characteristics of ideal insurable
exposures
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Expected Utility and the Demand for Insurance
This section extends the
discussion in Chapter 2.
Insurance Demand with Premium Loadings (Figure 19.1)
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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
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Deductible and Coinsurance (Insight 19.2)
Deductible
Insurer’s Share
Coinsurance
Coinsurance
Stop loss
Deductible
Insured’s Share
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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
pages 485-486
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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.
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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.
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Insurance Supply: Ideal Insurable Exposures
“Ideal” Insurable Exposures
Presence of numerous independent and identically
distributed (IID) units
Unintentional losses
Easily determinable losses as to time, amount, and type
Economically feasible premium
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Numerous IID Exposure Units
Each exposure unit in an insurance pool represents a
possible liability for the insurer. In the ideal case, these
exposure units 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.
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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)
Discussion in
pages 493-496
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Average Loss Distribution of an Insurance Pool (Figure 19.2)
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Probability of Ruin (Figure 19.3)
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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.
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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.
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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
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Discussion Questions
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?
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Discussion Question 1
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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.
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Discussion Question 4
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?
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