Question 1.

You have been asked to investigate whether the rate of ill-health retirement of the

employees of a large company varies with their duration of employment.

The company's records show:

? the date on which an employee was hired

? the calendar year in which they retired, if an employee left employment as a

result of ill-health retirement

? the date of retirement, if an employee reached the normal retirement age of 65

? the date of leaving, if an employee left the company for any other reason.

In the context of this investigation consider the following types of censoring and in each

case:

? describe the nature of the censoring

? state whether or not that type of censoring is present in these data

? if that particular type of censoring is present, explain how it arises.

(a) Left censoring

(b) Right censoring

(c) Interval censoring

(d) Informative censoring.

(i) Explain what it means for the last survivor status 50:60 to remain active for at least 10 years. (ii) Calculate the probability that the event described in part (i) occurs, assuming the two lives are independent with respect to mortality and: (a) the mortality of each life follows the ELT15 (Males) table (b) each life is subject to a constant force of mortality of 0.025 pa. (i) Explain what it means for the joint life status 50:60 to fail within the next 10 years. (ii) Calculate the probability that the event described in part (i) occurs, assuming the two lives are independent with respect to mortality and: (a) the mortality of each life follows the ELT15 (Females) table (b) each life is subject to a constant force of mortality of 0.025 pa. Given that ,4x =0.3 and ,q, =0.5, calculate ,,9xy and ,oxy - Consider each of the symbols listed below: (a) PXY (b) A xy (c) Explain carefully the meaning of each of these symbols and calculate the value of each, assuming that: (x) is subject to a constant force of mortality of 0.01 pa (v) is subject to a constant force of mortality of 0.02 pa the force of interest is 0.04 pa. A life insurance company issues 1,000 last survivor annuities to pairs of lives aged 60. Each pair comprises one male and one female, and the annuity pays $5,000 pa continuously until the second of the two lives dies. The single premium charged is $90,000. Calculate the expected present value of the profit to the life office and the standard deviation of this profit in respect of this group of policies. Basis: Mortality: PMA92C20 for the male life, PFA92C20 for the female life Interest: 4% pa effective Using this mortality assumption, Apreg =0.20021 at an interest rate of 8.16% pa