Economics of Insurance Lecture 3'

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Economics of Insurance Lecture 3.

• Demand for Insurance.
• Types of Insurance Contract

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Demand for Insurance
Excesses
Co-insurance
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Excesses
An excess is a fixed money sum that is deducted
from an insurance compensation payment as a
consequence of the terms of the contract.
For example, it is common for a contract to state
that the company will pay compnesation to the
value of the loss
MINUS
A fixed sum of money (the excess)
So a holiday insurance policy might state that
the insurance company will pay the value of
clothes and valuables lost or stolen on holiday
EXCEPT for the first 200
So a client whose clothes and other property to
the value of 1000 is stolen on holiday will
receive
1000 - 200 800
Another client whose clothes and other property
to the value of 500 is stolen on holiday will
receive
500 - 200 300
LUMP SUM DEDUCTION FROM COMPENSATION
The EXCESS deducted by the insurance company is
a
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Optimal insurance with an excess
Arrows second law of insurance.
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Assume fair insurance with an excess. i.e.
net comp rate odds but client agrees to pay
fixed amount for any claim e.g must pay first
200 of loss.
Demand for Insurance Excess
Arrows Second Law
X2
X1 X2 (Certainty line)
Insurance trading line. Slope net compensation
rate ( odds as rate is fair)
At a fair rate, a client always pays a full
premium, even with an excess
So paying less than full premium gives the client
less utility than paying full premium, even with
an excess
Excess lump sum payment
Optimum for full fair insurance without an excess
excess
Pays less than full premium
Full fair net comp
Utility at full insurance premium with excess
Pays full premium, but agrees excess
Net comp after excess
Pays less than full premium, and agrees excess
Utility at less than full insurance
Asset value, no insurance, bad event
Initial (uninsured) prospect
X1
Asset value, no insurance, good event
Full insurance
Note we have assumed the insurance company is not
allowing more than full insurance.
Suppose the client pays LESS THAN the full premium
Suppose the client pays the full premium
Full fair premium
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Demand for Insurance Excess
Limits of Arrows second law of insurance
INSURANCE COMPANY CHARGES A LARGE EXCESS
X2
The clients best insurance option is still to
pay the full premium
So the law doesnt hold if, with the excess, the
client wouldnt choose to insure
X1 X2 (Certainty line)
But now the excess is so large that the utility
from not insuring is greater than insuring. The
client wont insure at all!
Contract asks client to pay large lump sum excess
Optimum for full fair insurance without an excess
Excess
Utility with NO INSURANCE
Net compensation entitlement from full premium
payment
Initial (uninsured) prospect
Utility at full premium but
with large excess
X1
Full premium
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Co-insurance
Coinsurance is the sharing of insurance between
client and insurance company
(Note that this is US/UK usage. In continental
Europe the term is used more widely to mean any
sharing of insurance e.g. between different
insurance companies).
A co-insurance contract is one in which the
client pays a proportion of any compensation him
or her self.
Or the insurance company only pays a proportion
of the compensation due according to the premium
rate.
Say a client buys compensation at a particular
rate, e.g. 0.04 per compensation
But agrees to pay 20 of the compensation to
themselves
If the premium payment is 40
the compensation would be 80 of 40/0.04
800
i.e. 0.05 per net compensation
SO REALLY THE PREMIUM RATE IS 40/800
Putting the same point more generally, If a loss
of 500 was incurred
the compensation would be 80 500 400
The client is receiving less than full insurance,
but non-compensation element is PROPORTIONAL
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X2
Fair trade
Certainty line X1 X2
Some co-insurance
Co-insurance SWIVLES THE TRADING LINE
More co-insurance
Initial prospect

X1
The ANGLE between trade lines
represents the extent of the co insurance
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Demand for Insurance Optimal coinsurance
X2
Coinsurance causes effective divergence between
agreed odds and the company determined net
compensation rate
Thus the client chooses to UNDER INSURE
Full net compensation
Net compensation with coinsurance
Initial (uninsured) prospect
X1
Full premium
Premium with coinsurance
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NEXT LAW OF INSURANCE DEMAND
Coinsurance causes clients to change their
optimal levels of insurance
Companies should NOT expect demand for insurance
to remain the same when moving from insurance
company insurance to proportionately shared (CO)
insurance
This is quite different from the earlier example
of an EXCESS in which insurance companies would
not expect demand to change except in limiting
cases.
This is why companies can and do uses excess
clauses in contracts, but not, for ordinary
insurance, co-insurance provisions
Notice that with EXCESSES,
Companies can charge a FAIR rate, and still make
a profit.