Hello I understand that tP50aa is exp(-(lower case sigmax + mux)) but could someone please explain how to evaluate tP50ai (that is the probability of the life being ill at time t)? thanks in advance!
Hi Salma, tp50 ai represents the probability of being in the ill state at age 50+t given in the able state at age 50. Hence we need to calculate the probability the life has transitioned to the ill state before age 50+t and remained in the ill state to age 50+t. This requires an integral in terms of t for the transition into the ill state and another one in terms of s for remaining in the ill state once you have transitioned. The calculation of this would be pretty complex. Hence question 5.6 (as almost any question with this type of benefit would) is asking for you to put together an integral expression in terms of probabilities, rather than asking you to solve for any particular values. Hope this helps. Joe
