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A defined benefit pension scheme provides members with a single life pension at age 65, which increases each year in line with price inflation. At retirement, members can choose any of the following options: . Exchange up to 25% of the pension for an immediate lump sum, calculated as $15 for every fl per annum of the member's pension given up. . Swap the pension that increases with price inflation for a pension that increases at a fixed 3% per annum. . Reduce the member's pension by 10% in order to provide a spouse's pension on death of 50% of the member's pension at the time of death. (i) Discuss the issues that members should consider in deciding whether to exercise these options. [15] Current price inflation is 2% per annum and it is expected to remain around this level in the short term. (ii) Suggest why the scheme sponsor offers the option to choose fixed pension increases of 3% per annum rather than inflation linked increases. [3] List the other main retirement options that could be made available to the member at retirement. [2](i) Define the following types of stochastic process: (a) a Poisson process (b ) a compound Poisson process [3] Consider the modelling of the following situations: A the number of claims for motorcycle accidents received by an insurer's telephone claim line B the number of breakfast bagels sold by a New York bagel bar C the number of breakdowns of freezers in a large supermarket D the cost of wasted food caused by breakdowns of freezers in a large supermarket. (ii) Comment on which of the following stochastic processes will be most suitable for modelling each of the four situations above: time-homogeneous Poisson process . time-inhomogeneous Poisson process . time-homogeneous compound Poisson process . time-inhomogeneous compound Poisson process [6] [Total 9]