Financial services and their mathematical methods

Financial services and markets play a central role in today’s economy. As the past few years have shown, crashes in these markets and problems encountered by central ‘system-relevant’ financial institutions can endanger the prosperity of entire states, ultimately triggering crises in the global economy. It is therefore vital that we fully understand financial markets, their mechanisms and the risks involved. This necessitates the use of complex mathematical models and sophisticated statistical methods, as well as a profound understanding of economic interrelationships.

Institutes

Institute of Mathematical Finance
Profs Alexander Lindner, Robert Stelzer

Institute of Finance

Prof Gunter Löffler

Institute of Strategic Management and Finance

Prof Andre Güttler

Institute of Numerical Mathematics

Prof Karsten Urban

Institute of Statistics

Profs Jan Beyersmann, Markus Pauly
Institute of Stochastics

Profs Volker Schmidt, Evgeny Spodarev
Institute of Insurance Science

Profs An Chen, Mitja Stadje, Hans-Joachim Zwiesler
Institute of Economics
Profs Sebastian Kranz, Gerlinde Fellner-Röhling
Institute of Number Theory and Probability Theory
Prof Ulrich Stadtmüller

Contact

Prof Robert Stelzer, vice dean

Informative Literature

Risk Management and Insurance

Mathematics and economics - a unique combination

Thanks to its combination of subjects, almost unique in Germany, the Faculty of Mathematics and Economics is an excellent place to tackle such issues. Featuring a wide range of topics, the faculty is one of the world’s leading research institutions.

In this connection, it is not enough to simply consider traditional financial markets (equity, currencies, credit, interest…) and banks. The insurance industry is a major player among financial service providers. Not only must insurance companies be able to estimate insured risks as effectively as possible, they must simultaneously invest the premiums collected as profitably as possible on the financial market, particularly in the case of life insurance.

Another major scientific challenge is developing and exploring the methods and tools used by regulators and supervisory authorities (e.g. central banks, the American Securities and Exchange Commission, the British Financial Services Authority and the German Federal Financial Supervisory Authority Bafin) to monitor and control financial markets and financial institutions with the least possible effort. In the process, consideration must be given to the fundamental principles of the market economy, also ensuring maximum prosperity for society as a whole.

In addition to exploring traditional financial markets, a key element of our research activities involves studying and understanding energy, power and general commodity markets, and how to model them.

Success through interdisciplinarity

The range and complexity of the topics we investigate requires intensive cooperation between various areas of mathematics, management and economics. In our faculty, excellent researchers from the relevant subject areas conduct research side by side, engaging regularly in exchange and cooperating successfully in various research projects. One of the highlights of this close cooperation was the Research Training Group 1100 “Modelling, analysis and simulation in economathematics”, which was funded by the German Research Foundation (DFG) between 2005 and 2014. Successful interdisciplinarity is also closely connected to the Mathematics and Management study programme. When this programme was established at Ulm University at the end of the 1970s, it constituted a remarkable pioneer accomplishment. In fact, large parts of the professional examination to become an actuary can even be completed within this study programme.

Apart from the areas of mathematical finance, finance, insurance mathematics and insurance economics, numerous additional areas of the faculty play a central role in this key research area: stochastics and statistics thoroughly investigate models, enabling them to provide suitable methods. For example, extreme value theory and statistics is ideal for assessing risks. After all, extreme and very rare events are typically linked to the most hazardous risks. Owing to their rarity, for which we should be grateful, these events are difficult to understand. Spatial statistics is used to understand the spatial distribution of damages in various non-life insurance applications. The resulting mathematical models are often extremely complex. For this reason, cutting-edge methods of computation investigated and provided by numerical mathematics, are required in order to produce good results in an acceptable length of time. In turn, economics provides important insight into regulating markets.
One example of scientific issues that go beyond the core focus area is behavioural economics: players on financial markets by no means always behave rationally – the “Ulm Laboratory for Economics and Social Sciences” (ULESS) investigates the reasons for their decision-making behaviour. As an area of mathematics, optimisation provides answers to questions concerning interrelationships between financial markets, which are often highly complex networks.

Flooding in Ulm: an extreme, relatively rare natural phenomenon. How can we assess the risk posed by future weather events of this type and the damages caused?
Flooding in Ulm: an extreme, relatively rare natural phenomenon. How can we assess the risk posed by future weather events of this type and the damages caused?

Exemplary projects

Private pension insurance
What is the best way for me or my unit-linked private pension insurance to invest my pension contributions? What is the impact of the fact that I am unaware of my future income, making it a random amount?
For example, the Institutes of Insurance Science and Mathematical Finance joined forces to show that the popular advice along the lines of “the longer you have until retirement, the riskier you should invest" is not always true. In fact, the dependence between future income and the stock market is
essential.

Model reduction in derivative pricing
What is the right price for a derivative that is not traded on the market?
How can I determine the parameters of a model for a financial market such that it fits the observed market data as good as possible?
Pricing derivatives (options) is a typical issue in financial mathematics; in principle, you “only” have to compute an expectation. In sufficiently realistic models, however, expectation cannot be determined explicitly; it can only be determined numerically by solving very complex equations. The Institutes of Numerical Mathematics and Mathematical Finance are involved in a joint project to investigate how to perform these calculations as quickly and efficiently as possible. In particular, they are considering model reduction techniques. These allow models to be fitted quickly and precisely to market data in real time, i.e. without having to solve the complex equations again and again.

Contagion on financial markets
In recent financial crises, the risk of negative chain reactions was a frequently heard argument for rescue actions of governments and central banks. Measuring the magnitude of contagion effects, however, is a very difficult task.
Researchers at the Institute of Finance address the issue in several projects. In one of them, they examine the validity of newly proposed measures for the systemic relevance of banks. The analysis shows that some measures should be handled with care because they can give misleading signals in typical situations. The researchers also clarify the aspects that one should consider when using such measures, thereby contributing to the development of new and better measures.

What is the best way for me or my unit-linked private pension insurance to invest my pension contributions?
What is the best way for me or my unit-linked private pension insurance to invest my pension contributions?