# The Mathematics of Natural Catastrophes

**Abstracts**

**Steven Jewson **(Risk Management Solutions)

*Mathematical modelling of weather-related natural hazard risk in the insurance industry*

Over the last 20 years mathematical modellers in the insurance industry have developed a range of methods to model the financial risk due to natural hazards. These methods involve a mix of statistics, including extreme value theory; numerical modelling of the ocean, atmosphere and surface water; and data assimilation. They capture the risk due to hurricanes, extra-tropical storms, and thunderstorms. I'll describe briefly how some of these 'catastrophe models' are built, and what some of the outstanding modelling challenges are. I'll also review some of the contributions that state-funded research has made to catastrophe modelling, and speculate on how it might contribute in the future.

**David Stephenson **(University of Exeter)

*Clustering of Natural Catastrophes:statistical modelling of extra-tropical cyclones*

This talk will present an overview of our statistical research on the clustering of extra-tropical cyclones. The concept of random sums for modelling collective risk will be presented and key factors such as clustering of storms and the dependency between counts and magnitude will be presented. Extremes in aggregate losses due to multiple storms will also be briefly discussed.

**Chris Kilsby **(Newcastle University)

*Some aspects of modelling rainfall extremes in space and time*

A large number of applications in engineered infrastructure reliability and insurance require information on collective risk across large regions for present and/or future climates. For hydrological applications a simulation approach is often used so that Monte Carlo analysis may be carried out for systems with memory (e.g. river basins) or complex responses or operational rules (e.g. reservoirs). The presentation will cover examples of application of statistical models to cases where spatial or temporal dependence is important, including:

- Clustering of occurrence of rain storms in time (inter-annual variability) -Using a spatial Neyman-Scott Rectangular Pulses model for generation of rainfall fields covering large areas, some limitations and requirements

- Characterisation and modelling of extreme rainfall events covering large areas (e.g. whole UK)

**Chris Ferro **(University of Exeter)

*Probabilistic prediction of extreme weather events*

Probabilistic weather forecasts are typically based on multiple simulations from numerical weather prediction models. These simulations are produced by perturbing the initial conditions in order to explore the uncertainty that derives from imperfect knowledge of the state of the atmosphere. Statistical models are used to combine these simulations with past simulations and observations in order to produce probabilistic forecasts that are as well calibrated and precise as possible.

Several types of statistical model are commonly used, including regression, Bayesian model averaging and kernel dressing, and inference is conducted in a variety of ways. We investigate the performance of these different methods for predicting rare, extreme events and attempt to understand which features of the different methods have the greatest effect on performance.