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

The Cairns-Blake-Dowd (CBD) model for older ages is logit q(x,t) = κ1(t) + κ2(t)(x − x̄). Which description of its structure is correct?

The basic CBD model has two period-dependent factors, κ1 for the level and κ2 for the slope, with age entering through the fixed linear function x − x̄. It has no age-specific parameters and no cohort term, and κ are projected stochastically.

  1. AIt has a single period index and fixed age-specific parameters estimated for every age
  2. BIt has two period-dependent factors, with age entering through a fixed linear function of x − x̄Correct
  3. CIt includes a cohort term γ(t−x) as a core component
  4. DIt models the force of mortality as a Gompertz function with no time dependence
  5. It assumes κ1 and κ2 are deterministic constants

Explanation

In the basic CBD model, age enters only via the fixed linear term (x − x̄), and the two time-varying factors κ1 (level) and κ2 (slope) drive projections. It has no age-specific parameters and no cohort term in the basic form; κ are modelled as stochastic.

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