First 2 parts written till 7 marks is q1 From consider till down 3 parts is q2 Attempt both Thanksss in advance !

A unit-linked policy has the following profit vector: Year In-force profit 1 -25 2 -12 3 -6 4 25 5 35 (i) Calculate the reserves required, in order to zeroise the losses occurring at the end of years 2 and 3. Assume a rate of accumulation of 8% pa effective, and that qx = 0.01 at [2] each age. (ii) If the risk discount rate used is 10% pa effective, determine the net present value of the profits before and after zeroisation and state with reasons which of these figures you would expect to be greater. [5] [Total 7] Consider the following three-state illness-death model: Ox a = able Px VX d = dead Let op ik denote the probability that a life in state ; at age x will be in state k at age x+t, and let po denote the probability that a life in state ; at age x will remain in state j for at least t years. Given a constant force of interest of 8 pa, write down integral expressions for the expected present value of each of the following benefits payable to a policyholder who is currently aged exactly 50 and in the able state: (i) a benefit of 50,000 payable immediately on death, provided that death occurs within the next 10 years [2] (ii) a benefit of 50,000 payable immediately on death, provided that death occurs within the next 10 years and the life has been sick for at least a year at the time of death [3] a sickness benefit of 5,000 pa payable continuously throughout any period of sickness, ceasing at age 60. [2] [Total 7]