Jan Beirlant

Modelling censored losses using splicing: a global fit strategy with mixed Erlang and extreme value distributions

In risk analysis, a global fit that appropriately captures the body and the tail of the distribution of losses is essential. Modeling the whole range of the losses using a standard distribution is usually very hard and often impossible due to the specific characteristics of the body and the tail of the loss distribution. A possible solution is to combine two distributions in a splicing model: a light-tailed distribution for the body which covers light and moderate losses, and a heavy-tailed distribution for the tail to capture large losses. We propose a splicing model with a mixed Erlang (ME) distribution for the body and a Pareto distribution for the tail. This combines the flexibility of the ME distribution with the ability of the Pareto distribution to model extreme values. We extend our splicing approach for censored and/or truncated data. Relevant examples of such data can be found in financial risk analysis. We illustrate the flexibility of this splicing model using practical examples from risk measurement.

Estimating the maximum possible earthquake magnitude using extreme value methodology: the Groningen case

The area-characteristic, maximum possible earthquake magnitude

Mean-of-order p reduced-bias extreme value index estimation under a third-order framework

T_M

On the use of general linear mixed models in loss reserving

TM is required by the earthquake engineering community, disaster management agencies and the insurance industry. The Gutenberg–Richter law predicts that earthquake magnitudes M follow a truncated exponential distribution. In the geophysical literature, several estimation procedures were proposed, see for instance, Kijko and Singh (Acta Geophys 59(4):674–700, 2011) and the references therein. Estimation of

Reducing MSE in estimation of heavy tails: a Bayesian approach

T_M

Extreme value theory for (re-)insurance applications: Truncation, interval censoring and splicing

TM is of course an extreme value problem to which the classical methods for endpoint estimation could be applied. We argue that recent methods on truncated tails at high levels (Beirlant et al. Extremes 19(3):429–462, 2016; Electron J Stat 11:2026–2065, 2017) constitute a more appropriate setting for this estimation problem. We present upper confidence bounds to quantify uncertainty of the point estimates. We also compare methods from the extreme value and geophysical literature through simulations. Finally, the different methods are applied to the magnitude data for the earthquakes induced by gas extraction in the Groningen province of the Netherlands.