# Information Matrix

## Filter Information matrix

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### Real-time decision making

In a previous blog I looked at how continuous-time methods can provide real-time management information. In that example we tracked the (almost daily) development of the mortality of two tranches of new annuities, as shown again in Figure 1.

Figure 1. Cumulative hazard, \(\hat\Lambda(t)\), for new annuities written by French insurer. Source: Richards and Macdonald (2024).

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: Nelson-Aalen, Filter information matrix by tag: confidence intervals, Filter information matrix by tag: deduplication

### Real-time management information

The sooner you know about a problem, the sooner you can do something about it. I have written before about real-time updates to mortality estimates during shocks. However, real-time methods also have application to everyday management questions. Consider Figure 1(a), which shows a surge in new annuities in December 2014. The volume of new annuities written in that month was large enough to shift the average age of the in-force annuities, as shown in Fig

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: Nelson-Aalen, Filter information matrix by tag: annuities

### Portfolio mortality tracking: USA v. UK

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: season, Filter information matrix by tag: mortality shocks, Filter information matrix by tag: Nelson-Aalen, Filter information matrix by tag: OBNR, Filter information matrix by tag: reporting delays

### Visualising data-quality in time

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: data validation, Filter information matrix by tag: missing data, Filter information matrix by tag: Nelson-Aalen

### Mortality patterns in time

The COVID-19 pandemic has created strong interest in mortality patterns in time, especially mortality shocks. Actuaries now have to consider the effect of such shocks in their portfolio data, and in this blog we consider a non-parametric method of doing this.

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: season, Filter information matrix by tag: mortality shocks, Filter information matrix by tag: Nelson-Aalen

### Smooth Models Meet Lumpy Data

Most of the survival models used by actuaries are smooth or piecewise smooth; think of a Gompertz model for the hazard rate, or constant hazard rates at individual ages. When we need a cumulative quantity, we use an integral, as in the *cumulative hazard function*, \(\Lambda_x(t)\):

\[ \Lambda_x(t) = \int_0^t \mu_{x+s} \, ds. \qquad (1) \]

**Written by:**Angus Macdonald

**Tags:**Filter information matrix by tag: Nelson-Aalen

### The Karma of Kaplan-Meier

Our new book, *Modelling Mortality with Actuarial Applications*, describes several non-parametric estimators of two quantities:

**Written by:**Angus Macdonald

**Tags:**Filter information matrix by tag: Kaplan-Meier, Filter information matrix by tag: Nelson-Aalen, Filter information matrix by tag: Fleming-Harrington, Filter information matrix by tag: product integral