Suppose Jon has a utility of money function U=$ 1/2 ,he usually has an income of
ID: 340721 • Letter: S
Question
Suppose Jon has a utility of money function U=$1/2,he usually has an income of $100. but there is a 40%chance that his income will fall to $25. 1. How large an insurance premium would Jon be willing to pay in order to fully insure against this loss? 2.What is the minimym amount an insurance company could charge? 3. Now suppose Jon has a utility of money function U=5x$. He usually has an income of $100, but there is a 40%chance that his income will fall to $25. How large a premium would Jon be willing to pay in order to fully insure against the loss? 4. Finally suppose Jon has a utility of money function U=$2, he ususlly has an income of $100, but there is a 40%chance that his income will fall to $25. How large a premium would Jon be willing to pay in order to fully insure against the loss?
Explanation / Answer
First we have to understand what is expected premium and certainty premium.
Expected Premium is how much risk insurance company is covering up on estimated basis, while Certainty Premium is how much risk insurance company on algorithm basis.
1. Expected = 0.4(25)+0.6(100)
= 70
Certainty = (0.4(250.5)+0.6(1000.5))
e2 = 8
= 64
Minimum Premium Insurance Co. would be (100 - 70) + 0.5 = 30.5
Maximum Premium Insurance Co. would be (100 - 64) + 0.5 = 36.5
2.
Expected = 0.4(25)+0.6(100)
= 70
Certainty = (0.4(250.5)+0.6(1000.5))
e2 = 8
= 64
Minimum Premium Insurance Co. would be (100 - 70) + 5 = 35
Maximum Premium Insurance Co. would be (100 - 64) + 5 = 41
3.
Expected = 0.4(25)+0.6(100)
= 70
Certainty = (0.4(250.5)+0.6(1000.5))
e2 = 8
= 64
Minimum Premium Insurance Co. would be (100 - 70) + 2 = 32
Maximum Premium Insurance Co. would be (100 - 64) + 2 = 38
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