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…