Joan faces an 80% chance of having a loss of $0 and a 20% chance of having a loss of $10. Mary also faces an 80% chance of having a loss of $0 and a 20% chance of having a loss of $10. Harry faces a 80% chance of having a loss of $0 and a 20% chance of having a loss of $25.
What is the actuarially fair premium (AFP individually for Mary, Joan, and Harry)?
What is the COV for both Joan and Mary Individually?
What would the COV be for the insurance company be if they sold both Joan and Mary insurance for their AFP and they were in the same homogeneous risk pool?
If Harry is added to the risk pool for insurance. What would the expected loss be?
Explain if the pool is still homogeneous or not?
If the insurer charges all of them a price of $2.80, is that price a good deal for each of them? Why or why not? (hint – think about the AFP for each)