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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection

When fitting a Poisson Lee-Carter model, deaths D(x,t) are assumed Poisson with mean E(x,t)m(x,t). Which is a consequence of this assumption that is relevant to parameter uncertainty?

Under the Poisson assumption, parameters are estimated by maximum likelihood, and the inverse Fisher information gives approximate standard errors, which measure parameter uncertainty. The estimates are not exact, identifiability constraints are still required, and k(t) must still be projected.

  1. AParameters are estimated by maximum likelihood, and the inverse of the Fisher information gives approximate standard errors for the estimatesCorrect
  2. BThe variance of deaths is assumed to be constant across all ages
  3. CThe model needs no identifiability constraints on b(x) and k(t)
  4. DParameter estimates are exact, so only process risk remains
  5. The assumption removes the need to project k(t) in the future

Explanation

Poisson likelihood allows maximum likelihood estimation, with asymptotic standard errors from the information matrix, quantifying parameter uncertainty. Variance equals the mean, so it varies with exposure and rate. Constraints on b(x) and k(t) are still needed for identifiability, and k(t) still has to be projected.

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