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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models

For a life aged 40 in a select-and-ultimate table with a select period of 2 years, which statement about the notation is correct?

In select notation, [40]+1 means a life now aged 41 who was selected at age 40. So q_[40] is the first-year death probability after selection at 40, and q_[40]+1 is the rate one year later for the same life, differing from the ultimate rate q_41.

  1. Aq_[40] is the probability that a life who joined at age 40 dies within one year, and q_[40]+1 applies one year after selectionCorrect
  2. Bq_[40] and q_41 are always equal
  3. Cq_[40]+1 is the probability for a life selected at age 41
  4. Dq_[40]+2 is the select rate at duration 2
  5. l_[40] is the number alive at age 42 from a cohort selected at 40

Explanation

[x]+t denotes a life now aged x+t who was selected at age x. So q_[40] is the one-year death probability at selection and q_[40]+1 applies a year later to the same life, now aged 41. Option C confuses selection age with attained age. Option D is wrong because with a 2-year select period, duration 2 uses the ultimate rate q_42.

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