(Solution) - You have considered insuring a particular item of property such -(2025 Original AI-Free Solution)

Paper Details

You have considered insuring a particular item of property (such as an expensive camera, your computer, or your Stradivarius violin), but after considering the risks and the insurance premium quoted, you have no clear preference for either purchasing the insurance or taking the risk. The insurance company then tells you about a new scheme called ?probabilistic insurance.? You pay half the insurance premium quoted but have coverage only in the sense that in the case of a claim there is a probability of one-half that you will be asked to pay the other half of the premium and will be completely covered, or that you will not be covered and will have your premium returned. The insurance company can be relied on to be fair in flipping the coin to deter-mine whether or not you are covered.
a. Do you consider yourself to be risk-averse?
b. Would you purchase probabilistic insurance?
c. Draw a decision tree for this problem.
d. Show that a risk-averse individual always should prefer the probabilistic insurance.