Problem: Suppose that you are a healthy person and you buy a one-year insurance policy against becoming ill. You pay the fair expected value of this policy up front, which is a 1% chance that your expenses will be $100,000, so the premium you would pay is $1,000.
1) How would you characterize this transaction?
2) Now suppose another person has AIDS and knows that his expenses next year will be $100,000 for his treatment. From an insurance company's point of view, what would be the fair premium for this individual?
3) Suppose an insurance company offers him the ability to pay $100,000 up front to administer and pay all of his medical expenses for the next year. How would you characterize this transaction?