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…

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Tags: Lee-Carter, identifiability constraints, GLM

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