In this thesis, we firstly introduce the basic terminology and concepts needed for the the following chapters. In particular we introduce the basics of graph/network theory, epidemiological models (both well mixed and on ...

We demonstrate the effectiveness of an adaptive explicit Euler method for the approximate solution of the Cox-Ingersoll-Ross model. This relies on a class of path-bounded timestepping strategies which work by reducing ...

The thesis introduces a new method, the MC-Tree method, for pricing certain financial derivatives, especially options with high accuracy and efficiency. Our solution is to combine Monte Carlo (MC) method and Tree method ...

In the dynamic stochastic modeling of financial and economic time series, the concept of cointegration plays an important role. It refers to the existence of long-term equilibrium relations between variables in a dynamic ...

Distributional symmetries and invariance principles in noncommutative probability theory provide sufficient conditions for the existence of central limit laws. In contrast to classical probability theory, there exist many ...