Lecture 7 b

1
Economics of Insurance
Lecture 7 b
State contingent asset theory and insurance
2
INSURANCE as STATE CONTINGENT INCOME EXCHANGE
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 through
paying a premium R (thus reducing our assets if
event one occurs) but receiving NET COMPENSATION
C if event 2 occurs
3
INSURANCE TRADING LINE
Suppose the deal was that the insurance company
would pay 9 net compensation for every 1 of
premium paid. That is the NET PREMIUM RATE 1/9
0.111 or 11.1 pence per cover. We also would
say that the NET COMPENSATION RATE was 9.
Say PREMIUM 500, NET COMP would be 4500
Car worth 10,000 undamaged, 5000 damaged
We have a CHOICE OF TWO PROSPECTS INSURED
PROSPECT, NOT INSURED PROSPPECT
(9500,9500P1,P2)
(10000, 5000P1, P2).
4
Equation for insurance trading line
The general form of any straight line equation
gives us
X2 -rX1 D
We know r is the insurance company's net
compensation rate which equals 9  
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
5
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
6
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
7
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
8
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.
9
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.