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.

Mathematics for science and technology

Many modern developments in science and technology are inconceivable without the development and use of suitable mathematical methods and models. The latter form the subject of this research focus. Within the framework of a large number of interdisciplinary cooperations, especially with industry, a wide range of modelling and optimisation questions with an analytical-numerical, stochastic and discrete background are dealt with.

Quantitative economics

Subject of the third focus of research, quantitative economics, are the quantitative foundations of economic decisions in profit and non-profit organizations, with a special emphasis on the research activities and in the areas of risk management and sustainability research building on it.

In cooperation with medicine and psychology, we study behaviour-oriented research questions of economics and management.

Batteries for Electromobility

How can lifetime and performance of Lithium-ion batteries
in electric vehicles be improved? The Institute of Stochastics
investigates this kind of problems in cooperation with the
Helmholtz Institute Ulm for Electrochemical Energy Storage.

Answers are found by the combination of mathematical methods
from Stochastics, Physics and Numerics: stochastic 3D modelling
of complex microstructures (yellow/red) in porous battery
materials and their degradation, combined with physical modelling
and numerical simulation of charge transportation paths (blue)
in these microstructures.

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.

Sustainable Textile Industry

The initial idea of the project „Transformation of the Textile Industry towards Sustainability at the Location Dietenheim“ was to connect the sustainability-oriented urban revitalization of Dietenheim with the sustainable transformation of the textile supply chain. Eight textile companies have expressed their interest in participating and signed the declaration of intent. In the remaining project period an event template will be developed that enables Dietenheim to establish as a central place in terms of alternative textile concepts. Therefore, innovative business models will be methodological analysed and research on consumer behaviour will be conducted.

Interorganizational Networks

The competition within a market will change from company to value chain network competition in the future. Some best practice examples are complex supply chains, distribution cooperations or innovation (R&D) networks.

Companies face the challenge of optimizing the control mechanism of these networks. This includes the selection of the best network partners, best network location and the right controlling instruments as very important elements of the network management.

Therefore, we are working on solutions within a project to generate collaborations between plastics manufacturers for the exploitation of their production waste.

Expansion processes

Expansion processes occur in essentially every real world network. Examples are the spreading of a virus within a computer network or a society, or the propagation of a rumor within a social network. If the spreading is undesired as in the case of a virus, there are natural containment strategies that rely on the protection of individual nodes of the network. Graph theory offers a suitable setting to mathematically model and investigate such spreading and containment processes.

In this project we study the so-called irreversible dynamic monopolies as a simple graph theoretical spreading model and the firefighter game as a simple graph theoretical containment model. Our goals are structural and algorithmic results concerning these two fundamental notions and their variants.

Industrial Services

Due to decreasing product differentiation and lower profit margins, companies in the manufacturing sector are dealing with increasing competitive pressure. Therefore, industrial services like complex maintenance contracts or spare parts management have become a core offering.

They are attractive fort wo reasons: firstly, service offerings allow for differenciation from the competition. Secondly, they offer an attractive financial potential. Current research questions adress service management, the portfolio management of industrial services and incentive systems.