### Division of labour

#### (Jan 10, 2017)

At this time of year insurers have commenced their annual valuation of liabilities, part of which involves setting a mortality basis.  When doing so it is common for actuaries to separate the basis into two components: (i) the current, or period, mortality rates and (ii) the projection of the future path of mortality rates (usually mortality improvements).  This sub-division is carried over into the regular Solvency II assessment of capital requirements, where there is always a minimum of two sub-risks for longevity:

1. Mis-estimation risk, i.e. the uncertainty over the current level of mortality.
2. Trend risk, i.e. the uncertainty over the future direction of improvements.

In practice a Solvency II assessment…

### Further reducing uncertainty

#### (Jun 6, 2016)

In a previous posting I looked at how using a well founded statistical model can improve the accuracy of estimated mortality rates.  We saw how the relative uncertainty for the estimate of $$\log \mu_{75.5}$$ could be reduced from 20.5% to 3.9% by using a simple two-parameter Gompertz model:

$$\log \mu_x = \alpha + \beta x\qquad (1)$$

to "borrow" information at adjacent ages.  In the previous example we used just one year's data, whereas an obvious improvement would be to use the experience over multiple years to boost the data used.  Survival models for the force of mortality, $$\mu_x$$, can easily be extended to cover multi-year data, although we still occasionally see invalid applications of GLMs for qx

### (Mis-)Estimation of mortality risk

#### (Mar 2, 2016)

One of the risks faced by annuity providers is mis-estimation, i.e. the risk that they have incorrectly assessed the current rates of mortality.  This is often handled as a simple reduction factor applied to a published mortality table. There are two implicit assumptions behind this:

1. Mis-estimation risk is a constant proportion of mortality rates, and
2. Mis-estimation is a simple down-shift in rates without any offsetting aspects.

In fact the true situation is a lot more subtle than these two assumptions imply, as mortality risk can seldom be fully expressed with a single parameter.  Richards et al (2013) demonstrated this with a multi-parameter model covering seven risk factors.

Multiple parameters in…