PQ-4-331-2011-F

PQ-4-331-2011-F - Practice Questions 4 – ACTSC 331 FALL...

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Unformatted text preview: Practice Questions 4 – ACTSC 331, FALL 2011 1. Consider the accidental death model illustrated by the following figure: Dead - Accident 1 % μ 01 x + t Alive 0 & μ 02 x + t Dead - Other Causes 2 (a) Write down expressions or values of t p 00 x , t p 11 x , t p 22 x , t p 00 x , t p 11 x , and t p 22 x for t > 0. (b) Write down Kolmogorov’s forward equation for t p 01 x and derive the solution to t p 01 x for t > 0. (c) Write down Kolmogorov’s forward equation for t p 02 x and derive the solution to t p 02 x for t > 0. (d) You are given that the force of interest δ = 0 . 05 and the following transition intensities: μ 01 60+ t = 0 . 02 , μ 02 60+ t = 0 . 01 , ≤ t ≤ 10 . i. Calculate the probability that a life aged 60 is still alive at age 70. ii. Calculate the probability that a life aged 60 will die in the next 10 years due to an accident. iii. Calculate the probability that a life aged 60 will die in the next 10 years due to other causes....
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PQ-4-331-2011-F - Practice Questions 4 – ACTSC 331 FALL...

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