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That would only fix it if the risk was being taken with no benefit. If the person has a $5000 deductible and could spend $300 to prevent a 5% chance at $50,000 in damage, now they won't, because their expected value of the loss has gone from -$2500 to -$250, which is now better for them than paying the prevention cost.

It also makes incentives weird, e.g. with a $5000 deductible you'd prefer a 5% chance at $50,000 in damage (expected value -$250) over a 10% chance at $5000 in damage (expected value -$500).



5% of $50,000 is $2500


Which is why the expected value of the loss without insurance is $2500.

You have a 5% chance of losing $50,000 and a 95% chance of losing nothing. If you have insurance with a $5000 deductible, that becomes a 5% chance of losing $5000 and and a 95% of losing nothing. Expected value is the sum over all events of (probability of event) times (cost of event). 5% times $5000 is $250, 95% times $0 is $0, total with insurance is $250 instead of $2500. So you risk $50,000 over $300 at 5% probability because $45,000 of the risk is on the insurance company.




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