# Information Matrix

## Filter Information matrix

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### Compare and contrast: VaR v. CTE

Insurance reserving in many countries looks at extreme scenarios over a single year.

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: conditional tail expectation, Filter information matrix by tag: SST, Filter information matrix by tag: quantile, Filter information matrix by tag: percentile

### Conditional tail expectations

In a recent posting I looked at the calculation of percentiles and quantiles, which underpin many calculations for ICA and Solvency II. Simply put, an \(\alpha\)-quantile is the value which is not expected to be exceeded \(\alpha\times 100\)% of the time. This value is denoted \(Q_{\alpha}\). Mathematically, for a continuous random variable, \(X\), and a given probability level \(\alpha\) we have:

$$\Pr(X\leq Q_\alpha)=\alpha$$

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: conditional tail expectation, Filter information matrix by tag: quantile, Filter information matrix by tag: percentile, Filter information matrix by tag: coherence, Filter information matrix by tag: subadditivity

### Quantiles and percentiles

Quantiles are points taken at regular intervals from the cumulative distribution function of a random variable. They are generally described as q-quantiles, where q specifies the number of intervals which are separated by q−1 points.

**Written by:**Stephen Richards

**Tags:**Filter information matrix by tag: quantile, Filter information matrix by tag: percentile, Filter information matrix by tag: Solvency II, Filter information matrix by tag: Excel, Filter information matrix by tag: R language