Expail the ordinal utility approach.

12 points) XYZ Company sells Variable Annuity products, which include a Guaranteed Minimum Maturity Benefit (GMMB) rider and a "Guaranteed Minimum Cancer Benefit" (GMCB) rider which pays out a partial benefit acceleration upon diagnosis of cancer. Consider a contract offered to a person aged 50, with the following details: Single Deposit = 50,000 Maturity period = 3 years GMMB = 60% of total deposits, less any GMCB benefits paid GMCB = 60% x max[Fund Value, 100% of total deposits] at the time of cancer diagnosis. Management Charge Rate (m) = 0.70% of the Fund Value . Total Margin Offset (m, ) =0.30% of the Fund Value . Fund Value follows a lognormal model with / = 5% and o = 15% You are given the following mortality assumptions: 1 Pso = 0.9 IPS =0.8 1 PS2 =0.7 You are given the following with respect to cancer morbidity assumptions: 14, =0.01, for all ages , p, =80% of the , P, given above for mortality You are given the following from 100 scenarios generated from a standard normal distribution: Year 2 3 Scenario 1 0.483 -2.516 0.500 Scenario NPV (future liabilities) -includes all *in-the-money" scenarios 6 5834 17 1295 23 3095 29 789 44 4956 67 2094 95 567(a) (6 points) Calculate the net present value of future combined GMMB and GMCB liabilities for Scenario 1. Show your work. (b) (2 points) Calculate the 95% quantile, and the CTE95. Show your work. (c) (4 points) Describe three alternative models to the lognormal model