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

For a life aged 60, the survival probabilities are 1p60 = 0.98, 2p60 = 0.95, 3p60 = 0.90, and 4p60 = 0 (certain death before age 64). Assuming deaths are uniformly distributed between integer ages, what is the complete expectation of life e°_60?

The complete expectation is 3.33 years. The curtate expectation is the sum 0.98 + 0.95 + 0.90 = 2.83, and adding one half for uniformly distributed deaths gives 3.33. Trapezoidal integration of the survival function confirms this result.

  1. A2.83Correct
  2. B2.33
  3. C3.33
  4. D2.88
  5. 2.50

Explanation

Curtate e_60 = 0.98 + 0.95 + 0.90 = 2.83. Adding 1/2 for uniform deaths gives 3.33. Check via trapezoids: (1+0.98)/2 + (0.98+0.95)/2 + (0.95+0.90)/2 + (0.90+0)/2 = 0.99 + 0.965 + 0.925 + 0.45 = 3.33. The 2.83 option is the curtate value, which omits the half-year adjustment.

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