An insurance company has a portfolio of policies for which claims occur as a Poisson process at a rate of 50 claims per year. The individual claim amounts in s follow a log-normal distribution with parameters = 5 and o = 1. The insurer includes a premium loading of 15% on its premiums for this portfolio. a) Find the initial capital required in order to ensure that the probability of ruin at the end of the first year is 2.5%. You should assume that the aggregate claim amount for a year is approximately normally distributed. b) The insurance company decides to reinsure 30% of each risk in the portfolio by taking out proportional reinsurance with a reinsurer that loads its premiums by 25%. Find the new level of initial capital required to ensure that the probability of ruin at the end of the first year is still 2.5%.