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Show that (inx-p)- [4] 12no- A general insurance company writes claims, whose amounts have a lognormal distribution, with mean 300 and standard deviation 400. The insurance company purchases excess of loss reinsurance with retention 500 per claim. (ii) Calculate the average expected claim size payable by the insurance company. [6] Next year, claim inflation is 10%, but the retention amount remains the same. (iii) Explain whether the average expected claim size payable by the insurance company next year would increase by 10%. [2] ['Total 12] Consider the following time series model: Y, = 1+0.6Y,_1+0.167,-2+ 5, where & is a white noise process with variance of. Determine whether Y, is stationary and identify it as an ARMA(p,q) process. [3] (ii) Calculate E(F). [2] (iii) Calculate for the first four lags: the autocorrelation values P1. P2- P3. P, and the partial autocorrelation values V1, Vy, (;, W4. 171 [Total 12]Show that (inx-p)- [4] 12no- A general insurance company writes claims, whose amounts have a lognormal distribution, with mean 300 and standard deviation 400. The insurance company purchases excess of loss reinsurance with retention 500 per claim. (ii) Calculate the average expected claim size payable by the insurance company. [6] Next year, claim inflation is 10%, but the retention amount remains the same. (iii) Explain whether the average expected claim size payable by the insurance company next year would increase by 10%. [2] ['Total 12] Consider the following time series model: Y, = 1+0.6Y,_1+0.167,-2+ 5, where & is a white noise process with variance of. Determine whether Y, is stationary and identify it as an ARMA(p,q) process. [3] (ii) Calculate E(F). [2] (iii) Calculate for the first four lags: the autocorrelation values P1. P2- P3. P, and the partial autocorrelation values V1, Vy, (;, W4. 171 [Total 12]