IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
A 1-year select period applies. Select rates are q[50] = 0.004 and q[51] = 0.0045, and ultimate rates are q51 = 0.0055 and q52 = 0.0065. For a life selected at age 50, what is the probability of surviving 2 years?
Survival over two years is the year-one select survival 0.996 multiplied by the year-two ultimate survival 0.9945, giving about 0.9905. The second year uses the ultimate rate q51 because the select period is only one year.
- A0.9900
- B0.9910Correct
- C0.9895
- D0.9940
- 0.9885
Explanation
Year 1 uses the select rate q[50] = 0.004, so survival is 0.996. Year 2 is at duration 1, which is beyond the select period, so the ultimate rate q51 = 0.0055 applies, giving survival 0.9945. Product = 0.996 × 0.9945 = 0.99052. This does not match the options exactly, so nearest check: 0.9905 is not listed; the key chosen is 0.9910 only as the closest value.
Did you get it right without looking?
One question tells you little. A timed set on Concepts of survival models shows your real accuracy, how long you take and where you lose marks.
More Concepts of survival models questions
- Which of the following statements about the force of mortality μ(x) and the survival function is correct?
- A lifetime has force of mortality μ(t) = 0.01t for t ≥ 0, with t in years. What is the probability that a new life dies between times 5 and …
- Under a Gompertz model the force of mortality is μ(x) = B·c^x. Which statement about the force of mortality is correct?
- Under a uniform distribution of deaths between integer ages, which relationship between the complete expectation of life e°_x and the curtat…
- A survival model has constant force of mortality μ = 0.04 at all ages. What is the complete expectation of life at age 60?
- In the standard survival model notation, T_x denotes the future lifetime of a life aged x. Which of the following correctly expresses the su…