Response to the following problem:
Suppose a small fire insurance company insures 100 homes. Each homeowner pays an annual premium of $500. Fires are rare, but occur with probability 1 in 1000 per year. In the event of a fire, the insurance company must pay out $250,000.
a. Show that an expected value decision maker would enter this business.
b. Show that a worst-case scenario decision maker would run screaming in fear from this business.
c. How many years must an insurance company operate before the probability of losing money falls below 5%?
d. How much money must the insurance company have hoarded to survive these numbers of years?
e. If there were 1000 or 10,000 homes in the Book of Business, to what degree would your answers to (a) through (d) change?