An insurance company's business consists only of policies covering a specified event and which pay a sum assured of Z immediately on occurrence of this event. Claims on the portfolio of policies are considered to occur in accordance with a Poisson process with annual rate 2. The insurance company currently has assets of S (Z> S). It charges a premium which is to be 50% more than the expected outgo. Premiums can be assumed to be received continuously. The insurance company's expenses are small and can be ignored. (i) Derive the total annual premium charged by the insurance company on the portfolio. [1] (ii) Show that the probability that the insurance company has insufficient assets to pay the next claim made is given by: 1. 1-exp(-115(1-2)] [3] [Total 4]