IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Valuing cashflows contingent on multiple transition events
In a model with constant intensities, the holding time in state H has an exponential distribution with parameter equal to the total intensity out of H, 0.12 per year. What is the expected time spent in H before the first transition, to two decimal places in years?
The expected holding time is 1 divided by the total exit intensity of 0.12, which equals 8.33 years, since the waiting time is exponential.
- A8.33Correct
- B0.12
- C12.00
- D4.17
- 6.50
Explanation
The mean of an exponential with rate 0.12 is 1/0.12 = 8.33 years. Option 0.12 confuses rate with mean; 4.17 uses the median-like half.
Did you get it right without looking?
One question tells you little. A timed set on Valuing cashflows contingent on multiple transition events shows your real accuracy, how long you take and where you lose marks.
More Valuing cashflows contingent on multiple transition events questions
- Two independent lives have constant forces of mortality 0.03 and 0.05, and the force of interest is 0.04. A sum assured of Rs 90,000 is paya…
- In a service table, the only two decrements are death and withdrawal, with constant forces of decrement of 0.02 and 0.08 per year respective…
- Two independent lives aged 60 and 65 have survival probabilities over one year of 0.98 and 0.96 respectively. What is the probability that e…
- Independent lives (x) and (y) have constant forces of mortality 0.02 and 0.03, and the force of interest is 0.05. An annuity of Rs 12,000 pe…
- In a continuous-time multiple state model for a policyholder, the states are Healthy (H), Sick (S) and Dead (D). The policy pays a sickness …
- A policy has sum assured Rs 30,000 payable immediately on death and premiums of Rs 1,200 per year paid continuously. At a certain time the p…