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Applied Artificial Intelligence

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Mathematics

Viscosity Solutions on Ramified Spaces

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.

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Eikonal equations on ramified spaces

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.

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The vanishing viscosity limit for Hamilton–Jacobi equations on networks

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.

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Viscosity solutions of Eikonal equations on topological networks

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.

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Shortest paths and Eikonal equations on a graph

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.

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Granular Matter and the Time-dependent Viscous Eikonal Equation

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.

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Convexity of Surfaces Moving by Mean Curvature Flow

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.

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Risk Management in Banking

New Opportunities through Partial Use of the IRBA under CRR III

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%.

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Machine Learning for IRBA Rating Systems

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.

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Capital Relief through Optimized Use of the IRBA under CRR III

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.

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Interpretability of Machine Learning Methods in Credit Risk Measurement

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.

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Machine Learning Methods as a Benchmark for Classical Rating Approaches

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.

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