Flooding can have a severe impact on society causing huge disruptions to life and great loss to homes and businesses. The December 2015 floods across Cumbria, Lancashire and Yorkshire caused widespread damage and tens of thousands of properties were left without power. Governments, environmental agencies and insurance companies are keen to know more about the causes and the probabilities of the re-occurrence of such events to prepare for future events. Therefore we wish to better understand the flood risk and the magnitude of losses that can be incurred. My PhD project with JBA Risk Management is concerned with modelling such extreme events and estimating the total impact.

In order to assess the risk from flooding one needs to simulate extreme flood events, and improving upon the existing model for this is the main focus of the project. The simulation of flood events is important in understanding the flood risk and determining the loss distribution. Typically there is little loss history available and so extrapolation purely from this data would be unreliable. Thus, we instead consider the mechanism that leads to these losses, i.e. the extreme weather events. This part of the project is based on extreme value theory since we are interested in the events that create the greatest losses of which there may be little or no past data to extrapolate from. Extreme value theory is the development of statistical models and techniques for describing rare events. In other words, concern lies in fitting the tails of a distribution correctly unlike much statistical theory which is generally more focussed on the body of the distribution of interest.

I am considering four different areas of research within this setting:

- The bias we obtain when we decide to analyse data after an especially extreme event and how we can account for this.
- The development of an effective and efficient method for declustering (identifying events) in a multivariate time series.
- The development of a method which incorporates physical constraints such as the maximum rainfall possible.
- Building upon the Heffernan and Tawn model together with the areas above to develop a spatio-temporal model for the extreme flood events.

The second part of the project will be concerned with studying the tail of the loss distribution and improving the efficiency of estimation of the quantiles of this distribution. JBA's clients have portfolios containing a number of so-called risks. These risks include contents insurance or building insurance and therefore one property may have multiple `risks' associated with it. JBA's current procedure for calculating the loss is to simulate extreme events, use these to model the water depths (essentially) everywhere, and use these water depths to simulate the loss for each risk. Summing these losses over all the risks in a portfolio and over the simulated events in a year then results in simulation of the total loss for one year. However, this method is computationally expensive and so we wish to find a more efficient method to estimate this loss while retaining a reasonable degree of accuracy.

My project is supervised by Jon Tawn and Chris Sherlock at Lancaster University and Ye Liu at JBA.