A Bayesian Joint Model for Population and Portfolio-Specific Mortality

Insurers and pension funds must value liabilities using mortality rates that are appropriate for their portfolio. Current practice is to multiply available projections of population mortality with portfolio-specific factors, which are often determined using Generalised Linear Models. Alternatively, one of the well-known stochastic mortality models can directly be applied to portfolio data to construct portfolio-specific projections without the use of population data. However, this requires a sufficiently large historical dataset for the portfolio, which is often not available.We overcome this problem by introducing a model to estimate portfolio-specific mortality simultaneously with population mortality. We use a Bayesian framework, which automatically generates the appropriate weighting of the limited statistical information for a given portfolio and the more extensive information that is available for the whole population. It also allows us to incorporate parameter uncertainty when projecting portfolio-specific mortality rates.We apply our method to a dataset of assured lives in England & Wales. We find that uncertainty in portfolio-specific factors can be significant, and that confidence intervals for portfolio-specific mortality projections are slightly wider than those resulting from frequentist projections