Information Matrix

Our paper, "A stochastic implementation of the APCI model for mortality projections", was presented at the Institute and Faculty of Actuaries in October 2017. There was quite a discussion of the role of constraints in the fitting and forecasting of models of mortality. This got me wondering if constraints weren't in fact a red herring. This blog is a short introduction to the results of my investigation into the role, or indeed the non-role, of constraints in modelling and forecasting mortality.

Each year since 2009 the CMI in the UK has released a spreadsheet tool for actuaries to use for mortality projections. I have written about this tool a number of times, including how one might go about setting the long-term rate. The CMI now wants to change how the spreadsheet is calibrated and has proposed the following model in CMI (2016a):

\[\log m_{x,y} = \alpha_x + \beta_x(y-\bar y) + \kappa_y + \gamma_{y-x}\qquad (1)\]