Laying down the law

(Dec 14, 2010)

In actuarial terminology, a mortality "law" is simply a parametric formula used to describe the risk.  A major benefit of this is automatic smoothing and in-filling for areas where data is sparse.  A common example in modern annuity portfolios is that there is often plenty of data up to age 75 (say), but relatively little data above age 90.

For example, if we use a parametric formula like the Gompertz law:

log μx = α + βx

then we can use a procedure like the method of maximum likelihood to estimate α and β.  Once we have these values, we can generate mortality rates at any age we require, not just the ages at which we have data.

But which mortality law should one use?  In a recent paper (Richards,…

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Tags: log-likelihood, mortality law, CMI, Gompertz-Makeham family

Lost in translation

(Dec 30, 2009)

Actuaries have a long-standing habit of using different terminology to statisticians.  This page lists some common terms used by actuaries in mortality work and their "translation" for a non-actuarial audience.  The terms and notation are those used by actuaries in the UK, but in every country I have visited the local actuaries have used similar notation.

Table 1. Common actuarial terms and their definition for statisticians.

Actuarial term  Actuarial notation
Statistical description
central exposed to risk Ecx The time exposed to risk of dying at age x.
curve of deaths tpxmuxplust Probability density function for the future lifetime of an individual currently alive and aged exactly x.
force of mortality mux


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Tags: central exposed-to-risk, curve of deaths, force of mortality, initial exposed-to-risk, mortality law, mortality rate, survival rate, waiting time, survival models

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