Collective risk

This is my most active area of research. The name is an umbrella for several topics. One was a study of the railway line problem for JBA Consulting, from which emerged a paper on Why analyse inter-site dependence in river flooding? Recent work has been self-funded, with methods and results revealed in conference papers.

The characteristic theme is the extent to which risk estimates for different variables are partially dependent (i.e. correlated) due to spatial dependence in the physical processes giving rise to the extremes at each site.

It is often stated that inter-site dependence contaminates regional (i.e. pooled) estimates, and that this reduces the information content of a dataset. In turn, this erodes the certainty with which an extreme can be estimated.

While there is some truth in this view, it does not tell the whole story. Spatial (and temporal) dependence in a dataset of extremes is a natural by-product of the physical size (and longevity) of the extreme-producing physical conditions (often meteorological) causing the extremes. In some respects, the analyst should be just as worried about the absence of dependence in a dataset of extremes.

Dependence gives rise to three questions:

• How does the dependence interfere with the standard method for solving a classical problem (e.g. what is the 50-year 1-hour maximum rainfall in central Birmingham?)

• Can an understanding of the dependence help to improve estimates for the classical problem?

• What non-classical problems arise from the dependence?

Collective risk estimation is concerned with the last question: solving the non-classical problems that arise from dependence. It is quite a varied field. Examples include:

• Drought severity assessment

• Confluence flood estimation

• The railway line problem

• Catastrophe reinsurance

• Event rarity estimation.