Expected Value Insurance Claims

Question

Based on an insurance company's past data, each year an average of 1/90 policy holders make a claim of $250, 1/150 policy holders make a claim of $10,000, and 1/975 make a claim of $31,000.

 

What would the insurance company have to charge per policy-holder to break even? (i.e., what the premium would have to be in order to have an expected profit of zero.)

 

A vehicle insurance policy sells for $300 annually. What is the expected profit or loss for the company per policy-holder over the course of the year?

 

If the company sold 250 policies what would the overall expected profit or loss be?

If the company sold 250 policies what would the overall expected profit or loss be?

Answer 1

A vehicle insurance policy sells for $300 annually. What is the expected profit or loss for the company per policy-holder over the course of the year?

 

Using the given probabilities & claim payout amounts, we compute the per policy net income to the company as

300 -(1/90)(250) - (1/150)(10,000) - (1/975)(31,000) = $148.76

 

For 250 policies, the overall profit is $37,190.

 

The breakeven policy charge value is $101.24 = (1/90)(250) + (1/150)(10,000) + (1/975)(31,000) [to cover expected payout]