Up close and intimate with the APCI model

(Feb 12, 2019)

This blog brings together two pieces of work.  The first is the paper we presented to the Institute and Faculty of Actuaries, "A stochastic implementation of the APCI model for mortality projections", which will appear in the British Actuarial Journal.  The second is a previous blog where I examined the role of constraints in models of mortality.  The present blog combines the two and looks at the application of constraints to the CMI's APCI model.  I showed the results to a fellow statistician who expressed astonishment and even used the word "unbelievable"'.  So buckle up, and prepare to be astonished!

We use data on UK males from the UK's Office for National Statistics.  We have the number of deaths, $$d_{x,y}$$,…

Working with constraints

(Feb 9, 2016)

Regular readers of this blog will be aware of the importance of stochastic mortality models in insurance work.  Of these models, the best-known is that from Lee & Carter (1992):

$\log \mu_{x,y} = \alpha_x + \beta_x\kappa_y\qquad(1)$

where $$\mu_{x,y}$$ is the force of mortality at age $$x$$ in year $$y$$ and $$\alpha_x$$, $$\beta_x$$ and $$\kappa_y$$ are parameters to be estimated.  Lee & Carter used singular value decomposition (SVD) to estimate their parameters, but the modern approach is to use the method of maximum likelihood - by making an explicit distributional assumption for the number of deaths, the fitting process can make proper allowance for the amount of information available…