Question 1.28 (Developmental) An insurer has an excess of loss reinsurance arrangement in place with a retention limit of 50. Claim amounts (in f000s) have a Pareto distribution with parameters of = 2.5 and 1 = 350. (i) Find the mean claim amount paid by the insurer. [4] (ii) Find the mean claim amount paid by the reinsurer on claims in which the reinsurer is involved. [2] (iii) The insurer decides to investigate a proportional reinsurance arrangement with the reinsurer taking a proportion 0.3 of each claim. Find the percentage difference in mean claim amounts that the insurer will have to pay compared to using the excess of loss arrangement. [2] [Total 8] Question 1.29 (Exam-style) The loss severity distribution for a portfolio of household insurance policies is assumed to be Pareto with parameters c = 3.5, 1 =1,000. Next year, losses are expected to increase by 5%, and the insurer has decided to introduce a policyholder excess of $100. Calculate the probability that a loss next year is borne entirely by the policyholder. [3]