Stephen Richards Profile Picture

Stephen Richards

Managing Director

Articles written by Stephen Richards

One small step

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.
Tags: Filter information matrix by tag: log-likelihood, Filter information matrix by tag: numerical approximation, Filter information matrix by tag: derivatives

A model point

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.
Tags: Filter information matrix by tag: model points, Filter information matrix by tag: simulation

Forward thinking

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.
Tags: Filter information matrix by tag: survivor forward, Filter information matrix by tag: S-forward, Filter information matrix by tag: survival curve

Tables turned

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. 
Tags: Filter information matrix by tag: standard table

A rose by any other name

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
Tags: Filter information matrix by tag: cohort effect, Filter information matrix by tag: mortality projections

Between a rock and a hard place

The Advocate General of the European Court has recently opined that "the use of actuarial factors based on sex is incompatible with the principle of equal treatment for men and women".
Tags: Filter information matrix by tag: gender, Filter information matrix by tag: Solvency II

Putting the TAS into Longevitas

In the UK the Board for Actuarial Standards (BAS) has published a series of Technical Actuarial Standards (TAS).  At the time of writing there are three standards which are either in force or shortly will be: one for data (TAS-D), one for reports (TAS-R) and one for actuarial models (TAS-M).
Tags: Filter information matrix by tag: BAS, Filter information matrix by tag: TAS

Underflow

Earlier I described a problem in mathematical computing for mortality modelling.  This was where an intermediate step resulted in a number too big for the computer to handle, causing the entire calculation to overflow and fail. 
Tags: Filter information matrix by tag: floating point, Filter information matrix by tag: machine arithmetic, Filter information matrix by tag: precision

The bottom line

At it's core, the study of mortality is based on a simple ratio — the number of deaths, D, divided by the population exposed to the risk of death, E
Tags: Filter information matrix by tag: mortality projections, Filter information matrix by tag: Japan

History lessons

In the debate about how fast mortality will improve in the future, sometimes it is useful to remind ourselves how far we have come. 
Tags: Filter information matrix by tag: mortality projections