Question

Siobhan Roy has a$100,000 ring and keeps$100,000 cash in a checking account that paysno interest. If the ring is stolen, Siobhan will be forced to replace it at a cost of$100,000. Thechance of this happening is 1/100. She can, however, get insurance that would completelyreimburse to her the$100,000 if her ring was stolen.

What is the largest premium she would be willing to pay and what's the certainty equiv- alent of the event if her U-function is:
(i) U = y1/4
(ii) U = y*
(iii) U = Y?
where Y denotes the amount of cash she has. (Note that her utility function does not include the value of the ring, since she always has the ring.)

Answer 1

i) $4048.74

ii) $250.94

iii) $1000

Step-by-step explanation:

cost of ring = $100,000

P( stolen ring ) = 1/100 = 0.01

i) U = y^1/4

expected utility without insurance

Eu = 100,000^1/4 ( 0.99) + 0^1/4 ( 0.01 ) = 17.60

∴ largest premium equivalent utility = ( 17.60 )^4 = $95951.26

Largest premium = 100,000 - 95,951.26 = $4048.74

ii) U = y4

attached below

iii) U = Y

attached below