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The actuarial data onion

Actuaries tasked with analysing a portfolio's mortality experience face a gap between what has happened in the outside world and the data they actually work with.  The various difference levels are depicted in Figure 1.

Figure 1.  The actuarial data onion.

Written by: Stephen RichardsTags: Filter information matrix by tag: OBNR, Filter information matrix by tag: deduplication, Filter information matrix by tag: geodemographics, Filter information matrix by tag: survival analysis

Right-Censoring Rules!

A fundamental assumption underlying most modern presentations of mortality modelling (see our new book) is that the future lifetime of a person now age \(x\) can be represented as a non-negative random variable \(T_x\). The actuary's standard functions can then be defined in terms of the distribution of \(T_x\), for example:

\[{}_tp_x = \Pr[ T_x > t ].\]

Written by: Angus MacdonaldTags: Filter information matrix by tag: survival analysis, Filter information matrix by tag: right-censoring, Filter information matrix by tag: counting process

Why use survival models?

We and our clients much prefer to analyse mortality continuously, rather than in yearly intervals like actuaries used to do in previous centuries. Actuaries normally use μx to denote the continuous force of mortality at age x, and qx to denote the yearly rate of mortality. For any statisticians reading this, μx is the continuous-time hazard rate.
Written by: Stephen RichardsTags: Filter information matrix by tag: survival analysis, Filter information matrix by tag: survival models, Filter information matrix by tag: force of mortality, Filter information matrix by tag: hazard rate

Fifteen-year (h)itch

Effective risk modelling is about grouping people with shared characteristics which affect this risk.  In mortality analysis by far the most important risk factor is age, so it is not a good idea to mix the young and old if it can be avoided. 
Written by: Stephen RichardsTags: Filter information matrix by tag: survival analysis, Filter information matrix by tag: survival curve, Filter information matrix by tag: curve of deaths

Are you allergic to statistical models?

Or do you know someone who is? Some people are uncomfortable with the idea of statistical models, especially ones with parameters.
Written by: Stephen RichardsTags: Filter information matrix by tag: survival analysis, Filter information matrix by tag: Kaplan-Meier