IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models
Let K_x = floor(T_x) be the curtate future lifetime of a life aged x. Which statement is correct?
The probability that the curtate future lifetime equals k is kp_x times q_(x+k): the life survives k complete years and then dies within the following year. This is the deferred mortality probability k|q_x, and K_x takes only integer values.
- AP(K_x = k) = kp_x * q_(x+k)Correct
- BP(K_x = k) = kp_x * mu_(x+k)
- CP(K_x >= k) = (k-1)p_x
- DP(K_x = k) = k|q_x only for k = 0
- K_x takes non-integer values with positive probability
Explanation
K_x = k means survival for k full years then death within the next year: kp_x * q_(x+k), which equals k|q_x. Option 2 uses the force rather than the one-year probability, and P(K_x >= k) = kp_x, not (k-1)p_x.
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