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.

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.

Ship engines

Is it possible to optimize ship engines just by Mathematics?

The Institute for Numerical Mathematics and Voith Turbo Schneider Propulsion cooperate since 2005 on the topic of optimizing the Voith Schneider Propeller (VSP), a ship steering and propulsion system. Just using numerical simulations, the efficiency of the VSP could significantly be improved, which yields enormous savings in energy. In the meanwhile, we could simulate the movement of whole ships including real time control even in the rough sea.

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.

Decision Behaviour

How do people make decisions? What are the consequences of overconfidence of traders in the stock market? How can tax compliance be stimulated? Could social comparisons be a means to set incentives?

Standard models in economics assume that individuals are rational and selfish. In real life, however, psychological and social factors play a role when people make decisions. Behavioral economics helps to understand behavior: In the new "Ulm Laboratory for Economics and Social Sciences" (ULESS), we conduct choice experiments to discover behavioral regularities, improve theories and give advice to decision makers in firms and politics. 

Industry 4.0

What effect has the digitization on companies? The Institute of Technology and Process Management (ITOP) and the International Performance Research Institute (IPRI) find out the answer under the research focus "Industry 4.0 & Business Analytics.

Together with a large number of companies questions about Smart Production, Smart Services and Smart Networks are focused: How must corporate management change, so that the workpiece automatically finds his way through the workshop in a Smart Factory? What new Smart Services can be generated on the basis of customer data? How must purchase change, so that smart networks become reality?

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.

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.

Business Development

Which are the technology trends that will offer new business opportunities? How can companies assess theses chances and identify promising business areas? How can companies master the challenges they face when developing new business areas?

This research area focusses on application-oriented solutions that enables companies to access new innovative business areas. With a consortium of mid-sized companies, we develop solutions e.g. for manufacturers of industrial 3D-printers that no longer want to sell their products but aim to transform their business model to offering solutions.

Business Analytics

Corporate digitalization is evolving. Numerous sensors continually collect an extensive amount of different data within companies, such as status data of machines. What has also become more important in this context is the compilation of external data from social media.

The major field of study "Business Analytics" deals with the economic, mathematical and technological challenges of this development through a multidisciplinary approach. In projects, solutions are developed in cooperation with companies. These help, for example, travel operators to optimize their capacity planning based on social media data from potential customers.

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.

Spatial risk prediction in storm insurance

How does a storm insurance calculate its premiums? This and related questions concerning the coverage of dangerous storm risks are being studied at the Institute of Stochastics at Ulm University since 2007.

Answers can be found by using spatial claim models, where claim amounts are displayed in a topographic map. With the help of statistical methods it is possible to forecast the storm damage observed in different postal code areas. This provides a basis for the regionalized premium calculation.

Microstructure of porous materials

New solutions in automobile construction make use of lightweight materials, like for instance glass-fiber reinforced plastic. How can we detect unwanted cracks or production damages of the microstructure of such materials?

Within a project from the BMBF, the Institute of Stochastics at Ulm University currently works on this problem. The application of models from stochastic geometry allows for the analysis of the microstructure of these materials, and in particular the detection of inhomogeneities in the length and direction of the fibers in the system.

Dirichlet-to-Neumann operator

Boundary conditions play an important role in Analysis. In the case of Dirichlet boundary conditions the data are given on the boundary of a domain, whereas Neumann boundary conditions describe the flux through the boundary. In the project which is carried out by the Institute of Applied Analysis together with the University of Auckland (NZ), the Dirichlet-to-Neumann operator is the central object. New analytical properties are found, but also inverse problems are solved. Here one aims to identify parameters through measurements. This is in particular a central mathematical poblem of electrical impedance tomography. In fact, measuring electrical current on the surface of the human body, one tries to find out how the body looks inside.

Criminality forecasting

Prevention of mass crime such as burglary and theft is a challenge for the police in modern urban areas. The Institute of Stochastics (jointly with the State Police Office of Bavaria) deals with probabilistic analysis of spatial and temporal laws in mass crime since 2011. Using spatial regression and time series models, it is possible to make a statistical forecast of this kind of delicts.

Modeling of Biometric Underwriting Risks

All life and health insurance companies, as well as all companies offering occupational pension schemes, are not only exposed to the capital market risk which is caused by the uncertainty of the financial markets, but also in particular to the risk that probabilities of occurrence, such as probability of death or invalidation, are changing over time. Stochastic models are needed to quantify such risks. The development and calibration of these models constitutes an important part of our research. Thereby, we also deal with possibilities to manage the risk that is caused by the deviation of the actual development from the expected development. Our focus is the discussion of the longevity risk, which plays a central role in the context of “Ageing Societies”.

The methods of modeling such probabilities mathematically are applied to diverse economic questions, like for example the management of biometric risks, the pricing of longevity derivatives, the determination of risk capital under Solvency II, natural hedging and the evaluation of implicit options.

The Interaction of Real Estate and Labour Markets

The financial crisis has cast a spotlight on the interaction of real estate and labour markets. Do wealth losses, often in the form of reduced house prices, prevent people from becoming self-employed? Do high rates of home ownership impede migration out of the areas hardest hit by the crisis? The theoretical mechanisms underlying these questions are well understood and plausible, but are they empirically relevant? These are the questions we try to answer in our research at the Institute of Econimcs. The challenge here is to determine causality: Home owners are more succesful in the labour market than renters, even though they are less likely to move to find job; however, maybe people with better labour market prospects in their locality are more likely to become home owners. To disentangle these effects, we develop a range of new and innovative approaches.

Affiliated Research Institutions