Economics of Insurance 2

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Economics of Insurance 2

• Lecture 2

2
Differences of opinion between clients and
insurance companies on risks

• Asymmetry of information client and company

2)Knowledge are there priors or givens?
SO THERE IS NO GUARANTEE THAT CLIENTS AND
INSURANCE COMPANIES WILL AGREE ON TRUE
PROBABILITIES.
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Probabilities as presented by insurance companies.
Companies do not release there own estimates of
probabilities.
Why?
e(p) nG (i q)
so if a companys estimate of q is known then its
loading factor can be inferred

• Commercially sensitive with respect to other
  companies

2)Sensitive marketing information with respect to
clients.
SO EVEN IF COMPANY AND CLIENT AGREE BASICALLY ON
PROBABILITY, THEY WILL EFFECTIVELY DISAGREE IN
THE MARKET.
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So we are not likely to find situations
in which the market odds, offered by the company
in the form of a gross premium rate
is equal to the odds against a bad event as
perceived by clients
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So how can we analyse such situations.
REMEMBER INSURANCE WILL NOT BE PERCEIVED AS FAIR
BY THE CLIENT.
FIRST LETS REVISE HOW MUCH INSURANCE WILL BE
BOUGHT IN A FAIR DEAL
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Assume fair insurance i.e. net
compensation rate odds
X2
Arrows First Law of Insurance
X1 X2 (Certainty line)
Consider SCIC at intersection of constraint and
certainty line
Insurance trading line Slope net compensation
rate odds if fair
At a fair rate, a client always buys full
insurance
Only on certainty line does SCIC slope odds
So this is the only point at which the slope of
the SCIC slope of fair constraint ( odds)
So this is the optimum for fair insurance
Utility at full insurance
Utility at less than full insurance
Full fair net comp
Buy less than full insurance
Residual value (no insurance)
Initial (uninsured) prospect
X1
No Insurance
So buying less than full insurance gives less
utility than buying full insurance
Offered full Insurance
Full fair premium
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Now lets analyse demand for unfair insurance
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Unfairness to client implies (net compensation
rate lt odds) and (premium rate gt probability
of bad event)
X2
Unfair-to-client insurance implies under-insurance
FAIR TRADING LINE
X1 X2 (Certainty line)
UNFAIR Insurance trading line Slope net
compensation rate as determined by the
insurance company
So the client will prefer a smaller premium and
less compensation
State contingent indifference curve representing
expected utility of uninsured prospect
They will prefer to UNDER-INSURE or PARTIALLY
INSURE
Value damaged, fully insured
SCIC slope at certainty line odds against
event 2 (as perceived by client)
Certainty Equivalent
Optimal Insurance
Optimal value if damaged
Full insurance net compensation
Optimal net compensation
Value if damaged uninsured
Initial (uninsured) prospect
Consider FULL INSURANCE
X1
Value if undamaged and uninsured
Worst deal acceptable from clients viewpoint
Value undamaged fully insured
Certainty Equivalent
Optimal value of assets undamaged
Maximum premium client will pay
optimal premium
Unfair full insurance premium
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Unfairness to client implies (net compensation
rate lt odds) and (premium rate gt probability
of bad event)
X2
Summary Unfair-to-client insurance implies
under-insurance
X1 X2 (Certainty line)
Full insurance
v. OPTIMAL INSURANCE i.e. UNDER or PARTIAL
INSURANCE
Full Insurance
Optimal Insurance
Full insurance net compensation
Optimal net compensation
Range of insurance deals preferable to full
insurance
X1
optimal premium
Unfair full insurance premium
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Unfairness to client implies (net compensation
rate lt odds) and (premium rate gt probability
of bad event)
X2
Unfair-to-client insurance implies under-insurance
X1 X2 (Certainty line)
See if you can prove that, with the different
initial prospect shown below, the above law still
holds true. (Click to see some useful questions
to help you)
Where is the certainty equivalent?
Show the client would NOT buy full insurance
Is there a series of partial insurance deals
better than not insuring?
Where is the OPTIMUM and where are the optimal
premium and compensation amounts?
Initial (uninsured) prospect
Value if damaged uninsured
X1
Value if undamaged and uninsured