Assignment -

Information for questions 1 to 6 -

A life insurer is selling TPD policies to a superannuation fund which has 3,000 members.

The probability of total and permanent disability for any member is 0.002.

If any member becomes disabled they receive a benefit of $300,000.

You may assume that the claims are independent.

The insurance company charges a premium of $710 per member.

The company has initial capital of $950,000.

You may ignore expenses and investment income.

Question 1. What is the expected profit? Remember - no dollar signs, no commas in your answer.

Question 2. What is the expected return on equity? Please enter your answer as a percentage but with no % sign, e.g. if the answer is 12% please input 12 as your answer.

Question 3. What is the probability that the company will be insolvent at the end of the first year (i.e. unable to pay all the claims)? Please enter your answer as a percentage accurate to 2 decimal places but without the % sign, e.g. if the answer is 23.77229% please enter 23.77

Question 4. How much capital would the company need to ensure that the probability of ruin is below 1%?

Question 5. The company does not want to raise additional capital. Instead, the company considers buying quota share reinsurance, whereby the reinsurer takes 30% of the premium and agrees to pay 30% of all claims. What would be the revised probability of ruin?

Please enter your answer as a percentage accurate to 2 decimal places, without the % sign, e.g. if your answer is 11.8864% please enter 11.89

Question 6. The company decides NOT to buy any reinsurance. Instead, the company decides to increase the premium to $800 and offer a profit sharing agreement whereby the superannuation fund receives 15% of all profits (as long as the profit is positive). What would be the expected profit for the insurer (after paying the profit share)? [You might need to work this out using a spreadsheet, otherwise it is a bit tedious].

Information for questions 7 to 11

An insurance company sells household insurance. The insurance company has 1000 customers. For each customer, the number of claims in a year is a Poisson random variable with parameter 0.2. The claim size distribution is

Probability that the claim is $1000 - 0.90

Probability that the claim is $2500 - 0.10

The insurance company charges a premium of $240 for this policy.

The company has initial capital of $55,000.

You may ignore expenses and investment income.

The number of claims and size of claims are independent random variables.

Question 7. What is the risk premium for one policy?

Question 8. What is the expected return on equity for this company?

Please enter your answer as a percentage accurate to 2 decimal places but without the % sign, e.g. 23.7266% becomes 23.73

Question 9. What is the probability that the total annual claims cost for one customer is above $2100?

Please enter your answer as a percentage accurate to 2 decimal places.

Question 10. The company is considering buying excess-of-loss reinsurance policy. If any claim exceeds $1000, the reinsurer will pay the excess above $1200. What is the reinsurer's total risk premium for a reinsurance policy which covers the excess for all 1000 customers? [That is, what is the expected value of the total amount which the reinsurer will have to pay?]

Question 11. Assuming that the insurer does buy the excess -of-loss insurance policy. Of course the reinsurer will charge a higher premium than the amount calculated in the previous question, because the reinsurer also wants to make a profit. Suppose that the premium for the reinsurance policy is 180% of the amount calculated in the previous question. What is the probability of ruin for the insurer after allowing for the effect of reinsurance?

Please enter your answer as a percentage accurate to 2 decimal places.