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The run-off triangle below shows cumulative claims incurred on a portfolio of general insurance policies Development Year Policy Year 0 3 201 1 1.528 2,034 2,212 2,310 2012 1.812 2.251 2.951 2013 1,693 1,851 2014 2.125 Annual premiums written in 2014 were 4,023 and the ultimate loss ratio has been estimated as 916. Claims paid to date for policy year 2014 are 572. Estimate the outstanding claims to be paid arising from policies written in 2014 only, using the Bornheutter-Ferguson technique, stating any assumptions that you make. [9] A random variable X follows a gamma distribution with parameters o and 2. (i) Derive the moment generating function (MGF) of X. [31 (ti] Derive the coefficient of skewness of X. L8] [Total 11] Claims on a portfolio of insurance policies arrive as a Poisson process with annual rate ). Individual claims are uniformly distributed between 0 and 50, and the insurance company uses a premium loading of 12%. (i) Show that the insurance company's adjustment coefficient is 0.0066 to four decimal places. [3] The insurance company has entered into an excess of loss insurance agreement with a retention amount of M and with a reinsurer who uses a premium loading of 15% (ii) (a) Determine the mean amount per claim paid by the reinsurer as a function of M. (b) Determine the minimum retention level Mi for the insurance company, assuming that expected net premium income needs to be greater than expected net claims. [6] The insurance company manages to negotiate a lower reinsurance premium loading. (iii) Explain what happens to the minimum retention level Main, without doing any further calculations. [Total 11]