You consider buying insurance for your car for the next year. Your car is worth £15000. Historical data shows that you have 85% chance of not having any accident next year, 12% chance of having a minor accident, and 3% chance of having a serious accident, destroying the car. [For moral purposes, we assume your physical integrity not to be diminished, only the car is affected, not the persons inside]. The insurance company will pay the cost of the damage, which is estimated on average at £5000 for a minor accident, and of course the value of the car if it is destroyed. You adopt a risk-averse approach, with utility function U(x)=log(x+1000). We consider the insurance company to be risk-neutral. The cost of the insurance is £k. For which values of k (rounded) are both parties (you and the insurance company) happy to trade?
You consider buying insurance for your car for the next year. Your car is worth £15000. Historical data shows that you have 85% chance of not having any accident next year, 12% chance of having a minor accident, and 3% chance of having a serious accident, destroying the car. [For moral purposes, we assume your physical integrity not to be diminished, only the car is affected, not the persons inside]. The insurance company will pay the cost of the damage, which is estimated on average at £5000 for a minor accident, and of course the value of the car if it is destroyed. You adopt a risk-averse approach, with utility function U(x)=log(x+1000). We consider the insurance company to be risk-neutral. The cost of the insurance is £k.
For which values of k (rounded) are both parties (you and the insurance company) happy to trade?
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