State contingent asset theory and insurance

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Economics of Insurance
Lecture 7
State contingent asset theory and insurance
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Insurance 1 Lecture 7
Outline
Last week we looked out how an individuals
PREFERENCES towards RISK could be analysed using
Indifference curves
To use a more precise term, STATE CONTINGENT
INDIFFERENCE CURVES
Today we shall look at terms on which a client
can buy insurance
See how this is a budget constraint
Add our indifference curves to the analysis
And begin to draw some conclusions about an
individuals optimum level of insurance
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INSURANCE as STATE CONTINGENT INCOME EXCHANGE
Insurance 1 Lecture 7
Insurance can be thought of as the exchange of
one state contingent prospect for another.
On the diagram below
we move from ?1 to  ?2
X2
through paying a premium R (thus reducing our
assets if event one occurs)
but receiving NET COMPENSATION C if event 2 occurs
Prospect 2
Net compensation C
Prospect 1
X1
Premium R
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INSURANCE TRADING LINE
We want to insure our car worth 10,000
undamaged, 5000 damaged
The insurance company offers a NET PREMIUM RATE
1/9 0.111 or 11.1 pence per cover
or 9 net compensation for every 1 of premium
paid
(We could also say that the NET COMPENSATION RATE
was 9).
X2
We now have a CHOICE OF TWO PROSPECTS INSURED
PROSPECT, NOT INSURED PROSPPECT
(9500,9500P1,P2)
(10000, 5000P1, P2).
Insurance trading line
Slope -9
A line on the diagram joining those 2 prospects
Prospect insured
9500
Net compensation 4500
would have a SLOPE of
-9
Prospect 1
Prospect uninsured
5000
This is the BUDGET CONSTRAINT for the person
buying insurance
X1
9500
10000
Premium 500
Say actual PREMIUM paid 500,
NET COMP would be 9 x 500
i.e. 4500
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Finding an equation for the insurance trading line
Equation for insurance trading line
The general form of any straight line equation
gives us
X2 -rX1 D
SLOPE or GRADIENT of line net compensation rate
Why?
Because the slope is the ratio of ( net
compensation) premium
So r is the insurance company's net compensation
rate, which equals 9 in this case
so X2 -9X1 D
The line must go through the initial prospect
(10000,5000, P1,P2)
so
5000    -910000    D
so
D    95000          
X2    95000  -  9 X1
This is the equation for the insurance trading
line
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Insurance budget constraint
X2    95000  -  9 X1
  X2    D  -  rX1
This equation and the line it represents is a
BUDGET CONSTRAINT
X2
D 95000
SLOPE -r -net compensation rate -1/net
premium rate -9
insured
9500
Net comp
5000
No insurance
X1
10000
9500
premium
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Trading insurance line as a budget constraint
A smaller premium payment , say 200, would buy a
lower amount of compensation
Moving the individual less far up the trading line
X2
Cant insure to any point to the right of the
trading line, initial prospect not big enough
Previous insurance
9500
A smaller amount of insurance
lower net comp 1800
5000
No insurance
X1
10000
9500
Smaller premium - 200
The trading line thus shows the range of deals
possible at any one price
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Note that this example gives FULL insurance
Full Insurance
After insurance the prospect lies on the
certainty line There is no financial
uncertainty! Whatever happens, the client has
assets worth 9500
This is NOT however the general case.
X2
Certainty line
insured
9500
Net comp
No insurance
5000
X1
10000
9500
premium
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OPTIMUM Insurance
NOW WE CAN PUT TOGETHER THE STATE CONTINGENT
INDIFFERENCE CURVES
AND THE BUDGET CONSTRAINT
TO GET THE CLIENTS OPTIMAL INSURANCE DEAL
More on this later.
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Fair insurance
FAIR INSURANCE ALWAYS GIVES AN OPTIMAL LEVEL OF
INSURANCE FOR THE CLIENT ON THE CERTAINTY LINE
FAIR INSURANCE ALWAYS IMPLIES THAT THE CLIENT
WILL CHOOSE FULL INSURANCE.