The Semilinear Cahn-Hilliard-Gurtin System in Critical Spaces

In this thesis, the semilinear Cahn-Hilliard-Gurtin equation is studied using the method of Maximal Regularity. In 2012, Wilke developed a linear theory in $L^p$-spaces, and achieved a local and global well-posedness result for large $p$. In 2013, Denk and Kaip developed a linear theory in mixed integrability $L^pL^q$-spaces, using the method of...

Classifying Candida species using Mixed Integer Optimization based optimal classification trees

Global medical use of azole antifungals and echinocandins has led to an enormous increase in resistant <i>Candida</i> species, that are most commonly associated with fungal infections. A possible mechanism causing resistance are single or simultaneous point mutations in the genes responsible for encoding antifungal target enzymes. The aim of...

Forecasting the implied volatility surface in risk-management applications

In risk-management, one typically simulates many states of the market using models that are in line with historical data, also known as real-world models. For example, new regulations require insurance companies to value their position on a 1-year horizon. Insurance companies issue guarantees that need to be valued according to market...