IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)
In an illness-death model with constant intensities, healthy to sick is 0.04, healthy to dead is 0.01, with no recovery. Over a very short interval h, which approximation for the probability that a healthy life at age x is sick at x+h is correct?
The probability is approximately 0.04h, the healthy-to-sick intensity times the interval length. Transitions to death are a different state and are not counted, so using the total exit intensity of 0.05 would overstate the chance of being sick.
- A0.05h
- B0.04hCorrect
- C0.01h
- D0.04 + 0.01h
- 0.96h
Explanation
For small h, hp01(x) is approximately mu01 × h = 0.04h, with an error of order h². The 0.05h option is the probability of leaving healthy for any reason, which includes death.
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