1. Suppose a general insurance company is selling policies for motor vehicle insurance. The following is a schedule of the premium revenue for each quarter :
Quarter ending Premium revenue
March 2012  $56m
June 2012    $61m
September 2012 $63m
December 2012 $52m
Assume the premiums are received on average in the middle of each quarter. You are now required to determine the unearned premium provision for premiums written over the 2012 calendar year as at 31 December 2012. The insurance company assumes premiums are earned evenly over the year.

2. You are reviewing the reserves of a life insurance company and a general insurance company. In particular, you are reviewing the reserves of the 5 year endowment assurance policy portfolio for the life insurance company and the workers compensation insurance policy portfolio for the general insurance company. Answer the following questions :
(a) Discuss how the size of the reserves will vary for both insurance products over the life of the policy.
(b) Which product portfolio will have greater uncertainty in terms of claim payments? How would this impact on the level of reserves required for each portfolio?
(c) In terms of the 5 year endowment assurance policy reserves, how would the level be affected if the insurance company predicts the mortality of the policyholders has increased? Give reasons for your answer.
(d) Discuss the effects of inflation on the outstanding claims reserve estimates for both products. Why would you expect the effects to be different?
(e) Workers compensation claims may sometimes be subject to court disputes. Where the employer loses the court case, they may need to pay for the court fees on top of the settlement amount and the insurer may indemnify them under the cover. Suggest ways for the insurance company to factor such cases in their reserve estimates. Be specific in your answer by discussing what measures (claim amount, probability of a claim settlement) may be used in your estimation process.

3. Consider a general insurance company which has sold the following policies over the current financial year which ends on 30 June 2013, including the timing of the policy inception and premiums charged on each :
Product line                 No. of policies                Average inception                   Average premium
Motor vehicle                    1 000                         31 Dec 2012                                   $750
Home and contents                700                             31 Dec 2012                              $2 800
Public liability A                     1                              30 Sept 2012                                  $49 800
Public liability B                        1                            10 Jan 2013                                $42 500
For public liability policy A, this covered a marketing event which ran for 2 weeks starting on 15 October 2012. For public liability policy B, this covered an Australia Day concert.
(a) Calculate the total premium revenue expected to be received for policies sold this financial year.
(b) Draw a diagram to indicate how premium revenue is recognised over the life (the one year period between inception and the end of the cover) of each policy type given.
(c) Calculate the unearned premium provision for the policies. Assume for the motor vehicle and home and contents policies, the premiums are earned evenly over the year.
(d) From past experience, it is known that during the Christmas and Easter holidays, the number of claims increases due to higher number of car accidents and home break-ins. Based on this trend, how may you adjust your answer in b.) if you have access to monthly incurred claims data?