2. (20 points) An insurer plans to issue $50,000 whole life policies to lives aged 60. The policy is fully continuous (i.e. death benefit payable immediately at death and annual premiums G payable continuously throughout each year). Additionally, you are given the following information: i. ii. iii. Mortality follows the Standard Ultimate Life Table. The annual effective interest rate is 5%. Commissions expenses are 3% of premium in all years, paid continuously. There is an issue expense of $100 incurred at issue. 60 = 0.29743 260 = 0.113736 iv. v. vi. a. (4 points) Write an expression for the gross loss at issue random variable Lfor a single policy. b. (5 points) Write an equation for the E [L]] in terms of the gross premium G for a single policy. c. (5 points) Write an equation for the Var [%] in terms of the gross premium G for a single policy. d. (6 points) Determine the gross annual premium G, payable continuously, using the portfolio percentile premium principle assuming 1,000 policies and the Pr [L