Aggregate claims for a portfolio are assumed to follow a collective risk model. The number of claims is Poisson distributed with mean 50. Individual claim amounts are lognormally distributed with parameters = 6 and = 1.2247. (a) An insurer is considering a proportional reinsurance treaty with one reinsurer, under which the reinsurer pays 100(1 )% of every claim, where 0 < < 1. You are given that the reinsurer's expected aggregate claim cost is 6900. Show that the proportion of claims retained by the insurer is 0.84 to the nearest 0.01. Calculate the proportion of claims retained by the insurer to the nearest 0.0001. (b) Calculate the standard deviation of the reinsurer's aggregate claim cost under the proportional reinsurance contract. (c) Consider an alternative reinsurance treaty to the one considered in (a) and (b) that has the same expected aggregate claim cost, but a significantly higher standard deviation of aggregate claim cost. For which treaty would you expect a higher premium loading (amount of the premium that is in addition to the expected cost of claims), and why?