Expected Value – seller

Question

An insurance company sells a policy for $1000. Based on past data, an average of 1 in 100 policyholders will win a $20,000 claim on a policy, an average of 1 in 200 policyholders will win a $50,000 claim on a policy, and an average of 1 in 500 policyholders will win a $200,000 claim on a policy.

 

a. Find the expected value (to the company) per policy sold.

 

b. If the company sells 10,000 policies, what is the expected total profit or loss for the company?

Answer 1

they sold 10,000 policies at $1,000 each = $10,000,000

 

a maximum claim of $20,000 will happen 1 in 100 policies

so the maximum claim value will be $20,000 x (10,000 policies x 1 claim/100 policies) = $2,000,000

the net gain to the company would be $10,000,000 - 2,000,000 = $8,000,000

the expected value per policy sold = $8,000,000 ÷ 10,000 policies= $800

 

from this point, you can continue, using the information for the other possibilities.