Stephen Richards Profile Picture

Stephen Richards

Managing Director
Contact Stephen Richards

Articles written by Stephen Richards

Groups v. individuals

We have previously shown how survival models based around the force of mortality, μx, have the ability to use more of your data.  We have also seen that attempting to use fractional years of exposure in a qx model can lead to potential mistakes. However, the Poisson distribution also uses μx, so why don't we use a Poisson model for the grouped count of deaths in each cell?
Tags: survival models, Poisson distribution, GLM

Following the thread

Gavin recently explored the topic of threads and parallel processing.  But what does this mean from a business perspective?
Tags: parallel processing, simulation, Solvency II, technology

An early bath for the bathtub model

My last posting looked at why actuaries fitted survival models differently to statisticians, even though the conceptual framework for survival models is common to both disciplines.
Tags: survival models, mortality, bathtub hazard

Actuarial exceptionalism

In an earlier posting I listed some actuarial terms and their statistical equivalents (and later a short list of statistical terms and their equivalents in other fields).  Using different expressions for the same concept is an unfortunate barrier to understanding across disciplines.

Tags: survival models, left-truncation

Trend risk and age

There are several ways of looking at longevity trend risk, as covered in our recent seminar. However, regardless of how you choose to look at this risk, there are some pitfalls to watch out for.
Tags: Solvency II, ICA, longevity trend risk, model risk

2D or not 2D?

The Society of Actuaries (SOA) in North America recently published an exposure draft of a proposed interim mortality-improvement basis for pension-scheme work. The new basis will be called "Scale BB" and is intended as an interim replacement for "Scale AA".   Like Scale AA, the interim Scale BB is one-dimensional in age, i.e. mortality improvements vary by age and gender only. However, the SOA is putting North American actuaries on notice that a move to a two-dimensional projection is on the cards:

Tags: mortality improvements, Scale AA, Scale BB, trend reversal, CMI

Diet? What diet?

A while back I wrote about the lower life expectancy in Scotland. This has a number of drivers, but poor diet is one of them.
Tags: Scotland, diet

Ahead of his time

I'm giving away rather too much information about my age when I say I started work in 1990 right after graduating from university. Not long into my first job at a UK insurer, I was called to a meeting of the actuarial department.
Tags: Solvency II, use test, mortality projections

Longevity trend risk under Solvency II

Longevity trend risk is different from most other risks an insurer faces because the risk lies in the long-term trajectory taken by mortality rates. This trend unfolds over many years as an accumulation of small changes.
Tags: longevity risk, Solvency II, model risk

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.
Tags: survival analysis, survival models, force of mortality, hazard rate