Find the actuarial present value of an insurance policy

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Consider a multi-state model for the three lives (x), (y), (z) where we have eight states described below, where the stipulated lives are those still living,

State 0: all; State 1: (x), (y) only; State 2: (x), (z) only; State 3: (y), (z) only; State 4: (x) only; State 5: (y) only; State 6: (z) only; State 7: None.

You are given that μ01 = 0.02, μ02 = 0.01, μ03 = 0.04, μ34 = 0.02, μ35 = 0.06, μ36 = 0.05, μ67 = 0.10 and the force of interest is a constant 0.05.

(a) Find the actuarial present value of an insurance policy on the three lives which pays 1 at the moment of death of (z) provided that (x) dies first and (y) dies second.

(b) Find the probability that the lives die in the order (x), (y), (z).

Reference no: EM131001415

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