The financial crisis has shown that one needs to access and manage financial risk not only for individual financial institutions but also for the entire financial system as a whole. The goal is to reduce the likelihood that losses of some banks negatively affect the wider economy, and that, in order to mitigate contagion, costly government intervention and bank bailouts are necessary. I use probabilistic tools, such as random graphs, to analyze default contagion and fire sales in financial systems. I have obtained results that can be used to determine the final state of the system after a local shock propagates, to classify a given financial system as resilient/non-resilient to local shocks, and to determine capital requirements that ensure resilience of the financial system.
Welcome to the webpages of the Chair of Financial and Actuarial Mathematics!
Our group is dedicated to tackling cutting-edge research questions in financial and insurance mathematics. We actively contribute to both practical, decision-making-oriented research outcomes and more theoretical investigations. Some of our work necessitate delving into related inquiries within the domains of probability and data science/machine learning. Our current work revolves around three primary fields of research: Financial Systemic Risk, Infinite-Dimensional Stochastic Analysis with Applications in Energy Markets, and Machine Learning for Finance
Feel free to explore our website to learn more about our ongoing research, publications, teaching, and the passionate team behind these exciting endeavors.
At energy exchanges like NYMEX, CME, EEX and NordPool, one observes forward prices for different delivery maturities. This naturally leads to a curve that describes the current state of the market. Dynamic models are then typically defined based on some stochastic partial differential equation where the solution process takes values in a function space. My contributions in this area cover theoretical work in the area of infinite dimensional stochastic processes and stochastic partial differential equations, and more applied work that directly addresses the pricing and hedging of energy derivatives and calibration methods based on neural networks.
Machine learning has entered financial mathematics in the past few years. However, standard machine learning techniques are often not well suited to attack problems faced in financial mathematics. I am developing universal approximation results for neural networks in Fréchet spaces. These techniques are particularly suitable when dealing with functional data, a situation common in financial markets. I am also working on applications of these results for the pricing of flow derivatives and for PDE based option pricing.