-Steve owns a motorcycle valued at $5,000 and that is his only asset. There is a 5 percent chance that Steve will have an accident within a year. If he does have an accident, his motorcycle is worthless. Steve's utility of wealth curve is shown in the figure above. An insurance company agrees to pay Steve the full value of his motorcycle in case of an accident if he buys the company's insurance policy. The company's operating expenses are $500 per policy. What is the maximum insurance premium that Steve is willing to pay?
Definitions:
z
In statistics, 'z' often stands for the z-score, a measure of how many standard deviations an element is from the mean.
Standard Normal Random Variable
A random variable that follows a normal distribution with a mean of 0 and a standard deviation of 1.
Area
A measure of the extent of a surface or shape, calculated in square units.
z
A standard score that indicates how many standard deviations an element is from the mean of its distribution.
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