Applied Artificial Intelligence
Publications coming soon.
Mathematics
- 2006 Viscosity Solutions on Ramified Spaces Develops a consistent viscosity solution theory for Hamilton–Jacobi equations on ramified spaces (networks, LEP-spaces) – with correct transition conditions, comparison principle, and consistency with vanishing viscosity. Doctoral thesis, 2006.
- 2013 Eikonal equations on ramified spaces Generalization of the viscosity solution theory for Hamilton–Jacobi equations to higher-dimensional ramified spaces (LEP-Spaces). With Fabio Camilli and Claudio Marchi, 2013.
- 2013 The vanishing viscosity limit for Hamilton–Jacobi equations on networks Viscosity approximation for Hamilton–Jacobi equations on networks with Kirchhoff conditions at junction points — convergence to the unique solution of the original problem. With Fabio Camilli and Claudio Marchi, 2013.
- 2012 Viscosity solutions of Eikonal equations on topological networks Viscosity solutions for eikonal equations on topological networks — existence via representation formulas and uniqueness via comparison principle. With Fabio Camilli, 2012.
- 2012 Shortest paths and Eikonal equations on a graph Shortest paths from arbitrary points of a graph to a target node — an approach via eikonal equations and viscosity solutions on topological graphs. With Fabio Camilli and Adriano Festa, 2012.
- 2011 Granular Matter and the Time-dependent Viscous Eikonal Equation Derivation of a time-dependent viscous eikonal equation as a limiting case of the two-layer model for granular matter. With Karl-Peter Hadeler, 2011.
- 2001 Convexity of Surfaces Moving by Mean Curvature Flow Investigation of the invariance of convexity conditions under Mean Curvature Flow in general Riemannian manifolds. Diplomarbeit (Master's thesis), 2001.
Risk Management in Banking
- 2023 New Opportunities through Partial Use of the IRBA under CRR III CRR III allows banks for the first time to apply the IRBA selectively to individual credit classes – with potential capital savings of up to 27.5%.
- 2023 Machine Learning for IRBA Rating Systems Analysis of the EBA follow-up report on the application of machine learning in IRBA credit risk modelling – opportunities, challenges, and regulatory requirements.
- 2023 Capital Relief through Optimized Use of the IRBA under CRR III Strategies for capital optimization through targeted IRBA usage under CRR III – Output Floor, Partial Use, and their implications for capital planning.
- 2021 Interpretability of Machine Learning Methods in Credit Risk Measurement Methods for explainability of ML models in the regulatory context of credit risk measurement – from SHAP to XAI frameworks.
- 2018 Machine Learning Methods as a Benchmark for Classical Rating Approaches Comparison of ML-based and classical statistical rating approaches using ROC curves and Gini coefficients in the credit risk context.