### Constraints: a lot of fuss about nothing?

#### (Mar 5, 2018)

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.

We illustrate our argument with data on UK males from ages 40-104 and for years 1961-2015 from the Office for National Statistics (ONS). We have the number of deaths, $$d_{x,y}$$, age $$x$$ last birthday in year $$y$$…