Stochastics deals with events that we perceive as random or that can best be described as random due to chaotic behavior. It is a very broad field of research with diverse applications in physics, chemistry, biology, medicine, economics, insurance and finance.

Some examples are

• Financial mathematics: In this field, the prices of derivatives are determined. This takes into account the fact that a derivative or parts thereof can be replicated using suitable investment strategies.
• Network science: Networks are often used as an abstract description of complex relationships in technology, social and natural sciences. Of particular interest is the geometry of these networks and the behavior of processes that take place on these networks, such as the spread of viruses in computer networks. Such networks are often modeled by random graphs. In our research, we investigate both the properties of random graphs and the behavior of stochastic processes on them.
• Statistics: In order to fit models to data, model parameters must be estimated. The properties of the estimators are then examined in order to assess their quality and show that they lead to the correct models, at least asymptotically. A particular challenge today is dealing with very large amounts of data, for example when analyzing genome data. In addition, stochastic tests are being developed to test hypotheses or determine whether available data matches a particular model.
• Statistical mechanics: In statistical mechanics, macroscopic properties of physical many-body systems are derived from the microscopic behavior of individual particles using stochastic methods. Our research focuses on understanding the behavior of various models at phase transitions, such as the transition of a gas into the liquid state.
• Insurance mathematics: Here, the surplus of an insurance portfolio is modeled using stochastic processes. By using control variables, strategies are developed to optimize stability criteria or to maximize the benefits of life and pension insurance policies.

The Stochastics and Insurance Mathematics research area regularly organizes advanced seminars in which mathematicians from various universities give lectures. The current topics and dates can be found on the following page: Advanced Seminar Stochastics