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Some points for integration

The survivor function from age \(x\) to age \(x+t\), denoted \({}_tp_x\) by actuaries, is a useful tool in mortality work. As mentioned in one of our earliest blogs, a basic feature is that the expected time lived is the area under the survival curve, i.e. the integral of \({}_tp_x\). This is easy to express in visual terms, but it often requires numerical integration if there is no closed-form expression for the integral of the survival curve.

Written by: Stephen RichardsTags: life expectancy, survival curve, numerical integration, adaptive quadrature, Trapezoidal Rule, Simpson's Rule

(Mis-)Estimation of mortality risk

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.
Written by: Stephen RichardsTags: parameter correlations, orthogonality, mis-estimation risk

Sweet and sour

Public health initiatives, such as those being considered in the UK around sugar, carry risks as well as potential benefits for any government. The first consequence of action is the near-certain accusation of presiding over a nanny state.

Written by: Gavin RitchieTags: longevity, sugar tax, obesity, diabetes, health intervention

Working with constraints

Regular readers of this blog will be aware of the importance of stochastic mortality models in insurance work.
Written by: Stephen RichardsTags: Lee-Carter, identifiability constraints, GLM

The age pattern of mortality

Heligman and Pollard published a famous paper in 1980 with the title "The age pattern of mortality". In their paper they proposed an additive, three-component model of mortality:

\[q_x/p_x = f_I(x) + f_S(x) + f_A(x)\]

Written by: Iain CurrieTags: Heligman-Pollard model, accident hump, shape penalty, smoothness penalty

Old drugs, new tricks

Breakthrough science in the longevity space doesn't always require the development of new medicines. In fact, there are significant advantages to repurposing medicines already in use, since some of the most expensive aspects of drug development lie in establishing human safety in the trial phase.
Written by: Gavin RitchieTags: longevity, research, regenerative medicine, cognitive impairment, diabetes

The name of the game

We have written frequently on the importance of deduplication for mortality modelling.  In a mortality- or longevity-related transaction, it is critical that the risk-taker performs deduplication when fitting a statistical model to experience data.
Written by: Stephen RichardsTags: deduplication, names, National Insurance numbers, proportion married

Reverse Gear

Against a background of long-term mortality improvements it is understandable to expect that societal change and developments in health care will be agents of progress. Recent research from Princeton Professor of Economics Anne Case and Nobel prize-winning economist Angus Deaton jolts such complacency in the starkest way.
Written by: Gavin RitchieTags: longevity, mortality improvements, mortality plasticity, basis risk

A chill wind

In a previous blogs I have looked at seasonal fluctuations in mortality, usually with lower mortality in summer and higher mortality in winter.  The subject of excess winter deaths is back in the news, as the UK experienced heavy mortality in the winter of 2014/15, as demonstrated in Figure 1.

Written by: Stephen RichardsTags: season, influenza, winter, frailty, mortality plasticity

What — and when — is a 1:200 event?

The concept of a "one in two hundred" (1:200) event over a one-year time horizon is well established as a reserving standard for insurance in several territories: the ICA in the United Kingdom, the SST in Switzerland and the forthcoming Solvency II standard for the entire European Union. 
Written by: Stephen RichardsTags: Spanish influenza pandemic, mortality shocks, longevity shocks, Solvency II, ICA, SST, VaR, value-at-risk