1 (i) Define the following terms: (a) Working Layer (b) Stability Clause [2] (ii) Suggest why and when each of the above may be used. [4] [Total 6] 2 List the reasons why the risk based capital held by an insurance company (as a percentage of written premium) might vary from one line of business to another. [6] 3 You are the actuary for a small general insurance company that writes only personal lines motor business. Describe, with examples, the uncertainties relating to the estimates of the company s claims liabilities. [10] 4 You are the actuary for a UK general insurance company that writes only commercial motor fleet business. (i) Describe the variety of experience rating methods that could be used to set the risk premium for the different sizes of fleet. [6] (ii) Discuss the factors that you would take into account when determining the credibility factor, ignoring the effect upon the premium thus determined compared with the market or previous premiums charged. [2] (iii) (a) State the other components (non risk premium) of the theoretically correct premium rate. (b) Explain how they are loaded onto the risk premiums. (c) Suggest likely values for them. [10] At the beginning of 2004 the underwriting director suggests that the company s fleet rates are competitive and that during 2004 the company should write twice as much gross written premium as was written during 2003. You have been given the following information: Current solvency margin = 40% of premium written in the year Dividend distribution = 25% of the net insurance profit after tax Gross interest rate = 5% per annum Tax = 33% .

(iv) The directors wish to maintain the solvency margin at the current level of 40%. Calculate the required gross insurance profit for 2004 as a percentage of the gross written premium in 2004, defining the terms in any formula that you use. [3] (v) The finance director suggests a more conservative strategy. Strengthen the solvency margin required to 50% at the end of 2004 and assume profitability of 10% of gross written premiums which is in line with that achieved in 2003. Calculate the increase in gross written premium that this would permit. [2] (vi) State, with reasons, which of the strategies suggested in (iv) and (v) is most likely to be achievable. [4] [Total 27] 5 You are an actuary working for a general insurance company that writes only mortgage indemnity guarantee business. You have been asked to produce a document regarding the updating and revision of its business plan. (i) State the areas likely to be covered in such a document. [7] (ii) List the assumptions that you would need to make in preparing the plan. [6] (iii) Explain how you would determine the levels at which the assumptions should be set.

6 A general insurance company writes a portfolio of construction business that consists of civil engineering construction risks. Construction companies may insure building projects that have a planned duration of up to seven years with this insurance company. The insurer will pay for damage occurring during the construction process and building defects discovered for a short period after the building is handed over to the client. The insurance cover starts when the project commences and premiums are payable annually in advance. Premiums are based on the value of completed work and work that will be completed during the coming year. The company compiles monthly statistics on an underwriting year basis and all the premiums and claims are assigned to the underwriting year in which the project commenced. (i) List the perils that are likely to be covered by the policies described above. [2] (ii) Describe the features that you are likely to see in the premium and claim data triangles. [6] (iii) Describe the risks to the insurance company arising out of the premium and claim estimation processes. [9] (iv) The company cedes some of this portfolio to a reinsurance company. Under the terms of this treaty the insurance company provides half yearly bordereau to the reinsurance company (a) Explain what is meant by the term bordereau. (b) Describe the differences that you might see between the reinsurance company and insurance company premium and claim data triangles.

1 You are the actuary for a large well capitalised UK general insurance company. Discuss the following statements: (a) Where the mean term of the assets is less than the mean term of the liabilities a general increase in interest rates will adversely affect the solvency of the insurance company. (b) Capital values of UK equities are more volatile than the capital values of short term index-linked gilts. (c) The assets backing the free reserves should all be invested in short dated gilts. (d) Investment income from an equity portfolio will grow faster than the investment income from a portfolio of index-linked gilts.

2 Guidance Notes 18 and 33 have each been produced to assist actuaries in providing opinions required by the International Insurers Department and the New York Insurance Department in respect of business written in the United States of America. List the main differences between the two Guidance Notes in terms of purpose and content. [4]

3 In many countries insurers are required by law to maintain a minimum amount of capital in order to satisfy minimum solvency requirements. (i) Describe the following methods for determining minimum capital requirements: (a) Required Minimum Margin for a UK insurance company (b) risk based capital [3] (ii) Explain the advantages of the risk based capital method over the Required Minimum Margin method in (i) above. [3] [Total 6]

4 A private school, which charges its students school fees, would like to introduce a money back guarantee. Currently 100 pupils per year study for university entrance examinations with 80% achieving three or more top grades. The school would like to start an arrangement whereby if this level of three top grades isn t achieved by a pupil then the school fees are repaid in respect of that individual. Describe the risk factors which are likely to be relevant for such a portfolio of business.

6 You are an actuarial consultant who has been asked to review the premium rating calculations for a large household contents book of business. Suggest appropriate checks that should be undertaken to ensure that the risk premiums have been calculated correctly.

7 A large general insurance company writes a number of lines of business. For the past 30 years business written has included employers liability and public / product liability. It has been decided to cease writing these liability classes of business as at the end of next month. (i) Describe the risks the insurer might face from this liability book of business that could affect its profitability over the next 30 years. [15] (ii) It has been suggested that the insurer can mitigate some of these risks from this liability book of business by: (a) transfer of portfolio to a third party (b) adverse development cover Give a description of both the above solutions and state their advantages and disadvantages for the two main parties involved in each case.