You have been given the information from the mortality experience of a large life office

covering the years 2007 and 2008. Your information includes the number of people

aged x nearest birthday at 1 January 2007, 2008 and 2009, and the number of deaths

during 2007 and 2008 aged x nearest birthday. You have derived crude central rates of

mortality mx . State the assumptions that you had to make

A three-state Marl-tor.r mode] is represented by the following transition diagram: 51+, Hsalla _- pr+r Jul +.E The symbols 51+, , ,uJr +1 , #1\" and or +1 represent the forces of transition at age J: + I , where x is an integer and [lit-:21. The symbol Ipf, i=H,S,D, represents the probability that a life, who is in state i at age 1:, remains in state 1' until at least age x+t. {i} 1Write down the assumptions that are usually made when applying this model. [2] {ii} Derive the differential equation: a m m 5 IF): = _rpx (cl-1+: +r+rl and write down the relevant initial condition. [5] {iii} If 0'1\" = [1' and #1\" = p! for all 052' {1, show that: m?\" and\") [3]