Information Matrix

Last week we looked at how to compare mortality-improvement bases for pensions and annuities.  However, for many years some pension schemes in the UK did not have explicit mortality-improvement projections.  Instead, they allowed for mortality improvements by making a deduction from the valuation discount rate.

Which mortality-improvement basis is tougher — a medium-cohort projection with a 2% minimum value, or a long-cohort projection with a 1% minimum? Unless you are an actuary who works with such things, you have little chance of answering this question. 

It is often easy to be fooled into thinking that a small change is of little importance.  Small changes can persist over time, and sometimes it is only in retrospect that one realises just how big the accumulated change is.

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:

When fitting mortality models, the foundation of modern statistical inference is the log-likelihood function. The point at which the log-likelihood has its maximum value gives you the maximum-likelihood estimates of your parameters, while the curvature of the log-likelihood tells you about the standard errors of those parameter estimates.

It is an unfortunate fact of life that through time every portfolio will acquire data artefacts that make risk analysis trickier. Policyholder duplication is one example of this and archival of claims breaking the time-series is another.

The current issue of The Actuary magazine carries an article on the selection of model points. Model points were widely used by actuaries in the 1980s and 1990s, when computing power was insufficient to perform complex policy calculations on every policy in a reasonable time-frame.

A forward contract is an agreement between two parties to buy or sell an asset at a specified price at a date in the future. It is typically a private arrangement used by one or both parties to manage their risk, or where one party wishes to speculate.

Two years ago I asked the question whether we needed standard tables any more.  The question arose because most life offices and even many pension schemes have enough mortality-experience data to create their own portfolio-specific models. 

How important are the labels we give to things? In a seminal paper Richard Willets brought a particular mortality phenomenon to the attention of the UK actuarial profession