Question 10 In any particular year, the rate of investment return earned on the funds held by an insurance company is assumed to be independent of the rate of return earned in all previous years. Each year, the value of (1+it), where it is the rate of return achieved in year t, is lognormally distributed. (i) Given that the mean and variance of it are 0.05 and 0.052 respectively, determine the parameters and 2. [5 marks] (ii) Let S5 denote the accumulated amount after 5 years of an initial investment of one unit. State the distribution of S5. [1 mark] (iii) The insurance company will have to pay a liability of X in 5 years' time. If the company invests 1 million now, then the probability that the accumulated amount in 5 years' time will be sufficient to meet this liability is 95%. a) Calculate X. [4 marks] b) What is the expected amount of the surplus retained by the company after paying the liability? [1 mark]