Mathematical Methods for Risk Management

Risk Research at «RiskLab» of the ETH Zurich

Mathematical calculations of risk play a central role in the world of finance and insurance. «RiskLab» was founded in 1994 at the ETH Zurich and concentrates on applied research in risk management by encouraging closer co-operation between theory and practice. It is financed in the main part by the CS Group, the UBS and the Swiss Re and is established within the maths department of the ETH Zurich.

mju. Insurance representatives do not have it all their own way when they meet Uwe Schmock, as he himself admits, with a smile. The 40-year old from Berlin seems unassuming, even somewhat shy, but if anything remains unclear in the small print, one comes up against a brick wall. This mathematician knows about insurance questions; he is Research Director of «RiskLab» of the ETH Zurich, where a group of researchers are busy working on questions of risk assessment in finance and insurance branches.

Mathematical risk analysis

A risk remains a risk but its extent is becoming increasingly more calculable. Currently, the «RiskLab» researchers are working, amongst other things, on improving «modelling the dependence» of risk. Uwe Schmock The research director explains: banks, for example, know that a certain number of creditors will default. Often, this does not happen arbitrarily: natural catastrophes, for example, can destroy the harvest of an entire region and all farmers and growers in the region lose their livelihood. In «RiskLab» the researchers are developing models which enable banks and insurance companies to take such «shocks» into account.

At «RiskLab», as Uwe Schmock emphasises, while they work on concrete problems arising in the world of finance and insurance, the research carried out is strictly «pre-competitional». The researchers are not in the business of fulfilling contracts dictated by their sponsors; indeed, the big banks are not interested in new financial products which can be used by their competitors who also involved in the projects.

Advantages for both sides

Thanks to close co-operation between theoreticians and practice-oriented mathematicians, new methods, which are being developed in basic research within the branch of applied mathematics, can flow more quickly into hands-on research carried out at «RiskLab». Research results are freely available on the Internet ( and submitted to international specialist journals for publication. The researchers themselves present their results to specialists in finance centres and interested parties all over the world.

The institute also heightens interest in financial and insurance mathematics amongst the student body and ultimately elevates the quality of newcomers to the field for the companies who hire them after graduation. «RiskLab» also offers the employees of these companies the chance of keeping their knowledge of risk management up-to-date by organising specific courses and small conferences. At the same time, the connection with the world of finance and insurance has a fruitful effect on the world of research, as Uwe Schmock makes clear. In this way, scientists find out which areas are of particular interest to the end-users. Many researchers and professors are, according to Uwe Schmock, quite happy to add their knowledge to projects which are clearly linked to practice.

Eight research projects

Currently, eight research projects are running at «RiskLab». Five of these evolved from ideas brought in by researchers and professors from the participating universities (see below) and three were brought in by sponsors. One of the latter, which grew out of a suggestion from Swiss Re, deals with the following problem. Insurances have vast resources at their disposal, which they use to cover the claims of their clients. In their day-to-day business, they do not need these reserves. But why should an insurance company cover high risk clients while at the same time putting their «own money» under the equivalent of a mattress? If they courageously invest the company's money they take a risk - a risk which they must be able to evaluate accurately. Because, in the background, the rating agencies are waiting to demote a too courageous insurance company to a lower rating. In its turn, this is detrimental to the reputation of a company and its business. The customers of such companies begin to doubt whether their insurer has the wherewithal to cover any claims they might be forced to make.

For longer term forecast not dependable

Models to calculate the risk of investment for time frames of one or two weeks already exist, but for longer term forecasts, they are not dependable. Most insurance contracts run on an annual basis and insurance companies need risk values for the same period of time. This is precisely what "RiskLab" researchers are working on within the project described. For the time being, the running of «RiskLab» is limited to three years, but in view of the fact that 6 of the worst 40 catastrophes in the 30-year history of insurance occurred in 1999, we can safely assume that «RiskLab's» work will not run out any time soon.

A joint project of the ETH and the private sector

mju. «RiskLab» was founded in 1994 on the initiative of two ETH professors and - at the time - the three biggest Swiss banks to put the country's mathematical know-how at the disposal of the finance and insurance branches, while at the same time enhancing Switzerland's reputation as a country of research. In the beginning, the institute was only "virtual", mainly co-ordinating relevant research from a number of universities. After a re-organisation in 1999 the position of Head of Research was created and the institute moved into its own quarters at the ETH Zurich with, currently, nine researchers from all over the world. Further «RiskLab» employees work at partner universities. The Credit Suisse Group, UBS and Swiss Re help to finance research projects. The rooms and infrastructure, including two post-doctoral positions, are financed by the ETH. Co-operation within the ETH includes professors of Financial Mathematics, Operations Research, and Insurance Mathematics. Outside partners are the universities of Zurich, Lausanne and St. Gall and the INRIA-Institute in Sophia-Antipolis, France.

Freely translated from an article in: Neue Zürcher Zeitung, Ressort Zürich und Region, February 23, 2001, No. 45, page 45
(Links set by RiskLab, newspaper picture scanned)

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