The insurance premium will be equal to the expected loss, plus the profit margin for the insurance company.The expected loss is the probability of the loss times the magnitude of the loss, added up for all possible outcomes: 0.02*500,000 + 0.05*200,000 = 10,000 + 10,000 = 20,000Adding a 20% profit margin for the insurance company means we multiply this by 1.20:20,000*1.20 = 24,000The annual insurance premium is therefore $24,000.By "risk...
The insurance premium will be equal to the expected loss, plus the profit margin for the insurance company.
The expected loss is the probability of the loss times the magnitude of the loss, added up for all possible outcomes:
0.02*500,000 + 0.05*200,000 = 10,000 + 10,000 = 20,000
Adding a 20% profit margin for the insurance company means we multiply this by 1.20:
20,000*1.20 = 24,000
The annual insurance premium is therefore $24,000.
By "risk aversion parameter", I'm assuming you mean relative risk aversion parameter, which for y = 1 means that your utility function is logarithmic:
U = ln(C)
(As a reminder, normally it would be U = 1/(1-y) * (C^(1-y) - 1), but for y = 1 there is a special limit case which is U = ln(C).)
Ignoring all other spending, your consumption will be:
$76,000 if you buy insurance
$100,000 if you don't buy insurance and nothing happens (93% probability)
-$100,000 if you don't buy insurance and you get a small fire (5% probability)
-$400,000 if you don't buy insurance and you get a large fire (2% probability)
We can immediately see that you must buy the insurance, because your consumption goes negative and therefore your utility goes to negative infinity if you don't buy the insurance and you have a fire. You simply cannot afford to have a fire.
Under these conditions, your reservation price is actually $100,000. You are willing to spend all of your money to insure your house, because you cannot afford what would happen if you didn't.
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