Risk Analysis and Stochastic Modeling
Risk analysis is one of the most important issues in the financial world, but plays also a prominent role in engineering safety analysis and in the life sciences, in particular, in genetics and ecology. The basis for an adequate risk analysis is formed by appropriate stochastic models. The complexity of the processes involved calls for the use of sophisticated stochastic models beyond Gaussian models, allowing also for discontinuities in order to model abrupt changes.
Combining the expertise of both TUM and international fellows with those of distinguished scientists in the relevant application areas it is aimed to extend and deepen present research and to explore new areas of stochastic modeling and applications. In particular, it is planned to extend the focus of research to engineering, science and the life sciences. International cooperation will be intensified and new research partners, especially in the various application areas, will be acquired.
Prof. Claudia Klüppelberg is known for her expertise in extreme value theory and the stochastic modelling of risky systems and has developed methodology to assess and quantify risk in various areas (insurance, investment, operational, electricity, ...). During her time as Carl von Linde Senior Fellow she wants to extend the existing methodology to high-dimensional analysis and space-time modeling. She also works on applications in various fields, where a combination of stochastic modeling and numerical algorithms is a promising combination for risk quantification.
Prof. Robert Stelzer has intensively studied multivariate models driven by Lévy processes - both models especially designed for finance and, more general, time series models in continuous time. He has been working on Markov-switching models and the discrete approximation of Lévy driven stochastic differential equations. As a Carl von Linde Junior Fellow he was joined by several PhD students and worked on projects like “Extreme value theory and risk analysis for multivariate stochastic processes”, “Numerical methods for Lévy driven stochastic differential equations”, “Statistical analysis of Lévy driven continuous time processes” and “Properties of matrix-valued Lévy processes and matrix subordinators”.
Prof. Richard A. Davis (Columbia University, New York) is an expert in statistics for time series and extreme value theory for stochastic processes. He has coauthored several books, whose influence reach in every field of application. More recently he has done seminal work on space-time modeling, which is recognised world-wide. In connection with his Hans Fischer Senior Fellowship he was visiting TUM for several months during the summers of 2009, 2010 and 2011.
TUM-IAS funded doctoral candidates:
Martin Moser (PhD in 2012)
Oliver Pfaffel (PhD in 2012)
Eckhard Schlemm (PhD in 2011)
Christina Steinkohl (PhD in 2013)
Florian Ueltzhöfer (PhD in 2013)
Prof. Ole Eiler Barndorff-Nielsen (Århus Universitet) is well-known for his fundamental contributions to mathematical statistics and stochastic modeling with applications in various areas (e.g. quantum physics, the physics of wind-blown sand, turbulence, finance, ...). In recent years he has especially contributed to financial econometrics, the probabilistic theory of (free) Lévy processes and the stochastic modeling of turbulence. After he received a Humboldt Research Award in 2002 he has been visiting TUM for longer periods for several years and will continue to do so in the future.
Dr. Jean Jacod (Université Paris 6 Pierre et Marie Curie) has made important extensive contributions to stochastic calculus and limit theorems of stochastic processes. Moreover, he has substantially improved the understanding of the statistics of stochastic processes. Having received a Humboldt Research award in 2007, he visited TUM regularly for longer periods over the last years.
Publications by the Focus Group
- Eigenvalues of Large Random Matrices with Dependent Entries and Strong Solutions of SDEs. Dissertation, 2012 mehr…
- Estimation of Continuous-Time ARMA Models and Random Matrices with Dependent Entries. Dissertation, 2011 mehr…