Claims on a portfolio of insurance policies arrive as a Poisson process with annual rate ....

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Claims on a portfolio of insurance policies arrive as a Poisson process with annual rate . Individual claims are for a fixed amount of 100 and the insurer uses a premium loading of 15%. The insurer is considering entering a proportional reinsurance agreement with a reinsurer who uses a premium loading of 20%. The insurer will retain a proportion o of each risk. (i) (ii) Write down and simplify the equation defining the adjustment coefficient R for the insurer. [3] By considering R as a function of a and differentiating show that dR 100GR da, (iv) dR (120a-5)+120R 100R+100a- da dR (iii) Explain why setting = 0 and solving for a may give an optimal value da for a. Use the method suggested in part (iii) to find an optimal choice for a. FIR [3] [3] [4] Claims on a portfolio of insurance policies arrive as a Poisson process with annual rate . Individual claims are for a fixed amount of 100 and the insurer uses a premium loading of 15%. The insurer is considering entering a proportional reinsurance agreement with a reinsurer who uses a premium loading of 20%. The insurer will retain a proportion o of each risk. (i) (ii) Write down and simplify the equation defining the adjustment coefficient R for the insurer. [3] By considering R as a function of a and differentiating show that dR 100GR da, (iv) dR (120a-5)+120R 100R+100a- da dR (iii) Explain why setting = 0 and solving for a may give an optimal value da for a. Use the method suggested in part (iii) to find an optimal choice for a. FIR [3] [3] [4]

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