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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)

A study of 200 policyholders in an Indian insurer records 8 deaths over a total of 1,600 life-years of observation. Assuming a constant force of mortality, the maximum likelihood estimate of mu and the estimated variance of the estimator (approximately d/V^2) are respectively:

The estimate is 8/1600 = 0.005, and the approximate variance is d/V^2 = 8/1,600^2 ≈ 0.0000031. Dividing deaths by lives instead of by waiting time would wrongly give 0.04.

  1. A0.005 and 0.0000250
  2. B0.040 and 0.0000250
  3. C0.005 and 0.0000031Correct
  4. D0.005 and 0.0050000
  5. 0.040 and 0.0000031

Explanation

MLE = d/V = 8/1600 = 0.005. Variance ≈ d/V^2 = 8/2,560,000 = 0.000003125, about 0.0000031. The option with 0.0000250 uses d^2/V... mistakes such as 8/200=0.04 use number of lives instead of exposure.

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