IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
When projecting mortality with a CBD model, κ(t) = (κ1(t), κ2(t)) is commonly modelled as a two-dimensional random walk with drift. What is the main consequence for projected mortality?
With κ modelled as a two-dimensional random walk with drift, uncertainty about future mortality widens as the projection horizon grows, and the innovations in κ1 and κ2 may be correlated through a covariance matrix. Future values also depend on the latest fitted κ.
- AProjected rates are deterministic with no uncertainty
- BUncertainty about future rates grows with the projection horizon, and κ1 and κ2 changes can be correlatedCorrect
- CFuture κ values are independent of the current κ
- DThe two components must have the same drift
- Mortality at all ages is forced to converge to zero
Explanation
A random walk with drift has variance increasing linearly with time, so projection uncertainty widens. A multivariate version has a covariance matrix allowing correlated innovations between κ1 and κ2. Future values depend on the current value, so independence is false.
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