# Information Matrix

## Filter Information matrix

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### Robust mortality forecasting for 2D age-period models

The covid-19 pandemic caused mortality shocks in many countries, and these shocks severely impact the standard forecasting models used by actuaries. I previously showed how to robustify time-series models with a univariate index (Lee-Carter, APC) and those with a multivariate index (Cairns-Blake-Dowd, Ta

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: outliers, Filter information matrix by tag: coronavirus, Filter information matrix by tag: forecasting, Filter information matrix by tag: mortality projections

### Unpoking the bear

**Written by:**Gavin Ritchie

**Tags:**Filter information matrix by tag: immunotherapy

### M is for Estimation

In earlier blogs I discussed two techniques for handling outliers in mortality forecasting models:

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: outliers, Filter information matrix by tag: robustness, Filter information matrix by tag: log-likelihood

### Measuring liability uncertainty

Pricing block transactions is a high-stakes business. An insurer writing a bulk annuity has one chance to assess the price to charge for taking on pension liabilities. There is a lot to consider, but at least there is data to work with: for the economic assumptions like interest rates and inflation, the insurer has market prices. For the mortality basis, the insurer usually gets several years of mortality-experience data from the pensi

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: mis-estimation risk, Filter information matrix by tag: covariance matrix, Filter information matrix by tag: log-likelihood

### Understanding reviewers - a guide for authors

I recently came across an online article by W. S. Warren, the deputy editor of *Science Advances*. In the article Warren outlines some easy ways for submitting authors to improve their paper's chances of being accepted for journal publication.

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: academic publishing

### The Mystery of the Non-fatal Deaths

In the course of a recent investigation, with my colleagues Dr Oytun Haçarız and Professor Torsten Kleinow, a key parameter was the mortality rate of persons suffering from Hypertrophic Cardiomyopathy (HCM), an inherited heart disorder characterized by thickening of the left ventricular muscle wall. It is quite rare, so precision is not to be expected, and indeed an annual mortality rate of 1% \((q_x=0.01)\), independent of age \(x\), is widely cited. I

**Written by:**Angus Macdonald

**Tags:**Filter information matrix by tag: data quality, Filter information matrix by tag: data validation

### White Swans and the Moron Risk Premium

Interest rates and gilt yields are critical drivers of pension-scheme reserving and bulk-annuity pricing. However, many UK pension schemes self-insure when it comes to economic risks, with Liability Driven Investment (LDI) a common approach. This makes the turmoil in the UK Gilts market in Autumn 2022 of particular interest. Daily movements of 10-20 standard deviations arose as the

**Written by:**Patrick Kelliher

**Tags:**Filter information matrix by tag: gilt yields

### Normal behaviour

One interesting aspect of maximum-likelihood estimation is the common behaviour of estimators, regardless of the nature of the data and model. Recall that the maximum-likelihood estimate, \(\hat\theta\), is the value of a parameter \(\theta\) that maximises the likelihood function, \(L(\theta)\), or the log-likelihood function, \(\ell(\theta)=\log L(\theta)\). By way of example, consider the following three single-parameter distributions:

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: mis-estimation risk, Filter information matrix by tag: log-likelihood

### Turning Back The Clock

**Written by:**Gavin Ritchie

### Walking the Line

In mortality forecasting work we often deal with downward trends. It is often tempting to jump to the assumption of a linear trend, in part because this makes for easier mathematics. However, real-world phenomena are rarely purely linear, and the late Iain Currie advocated linear adjustment as means of judging linear-seeming patterns. This involves calculating a line between the first and last points, and deducting the line value at ea

**Written by:**Stephen Richards