Generating Asset Paths for Financial SDEs with GANs

Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. This thesis investigates if GANs can be used to provide a strong approximation to the solution of stochastic differential equations (SDEs) of the Ito type. Standard GANs are only able to...

The Lamperti Transform: Applications to Stochastic Local Volatility Models

This thesis showcases a rather contemporary method of solving a generalized system of stochastic differential equations (SDE's) comparable to the SABR model. The solution is derived from a stochastic-local volatility (SLV) model in which the local volatility (LV) component is kept general. This generality is maintained throughout all derivations...

Where does plastic in the ocean come from?: Using the end location to find the likelihood of a possible start location of plastic particles in the ocean

In the ocean resides a large amount of plastic. This has severe environmental consequences for the oceans. To be able to clean up all this plastic the location of the plastic is needed. A lot of times plastic is cleaned up at the source, but to clean up here this location needs to be known. However, what if the start location is not known and...

A numerical Fourier cosine method for forward backward stochastic differential equations with jumps

In financial and egineering problems, we are often faced with solving Partial-Integro Differential Equations (PIDEs). Rarely we can find an analytic solution in a closed form expression for these PIDEs, hence we turn to numerical schemes to accurately approximate the solution instead. Classically these methods are based on finite difference...

Likelihood-based Inference on Nonlinear spaces: Using Diffusion Processes on Riemannian Manifolds

When data in higher dimensions with a certain constraint on it, say a set of locations on a sphere, is encountered, some classical statistical analysis methods fail, as the data no longer assumes its values in a linear space. In this thesis we consider such datasets and aim to do likelihood-based inference on the center of the data. To model the...

The moving and settling of plastic in the ocean: Forward and reverse time modelling of plastic particles

The growing amount of plastic pollution in the oceans is worldwide a huge problem. There is an increasing amount of projects that try to clean up this pollution. To remove the pollution efficiently, it is useful to know how plastic litter moves, degrades and sinks. Models are being developed that can describe what happens with plastic in the...

Particle models for sand transport in water: analysis and simulations

This thesis describes how the simple random walk particle model can be extended to account for sand deposition and suspension, and for particle interaction: clumping together and falling apart. The extended models are analyzed, and the corresponding partial differential equations are derived. These equations are compared to the currently used...

Grey-box models for prediction and control of solar district heat plants

It has become clear that the global energy system needs to shift away from fossil fuels towards clean, renewable energy sources. Experience in the past decades has shown that at-plate solar heat panels can play a role in the energy system of the future, in particular in solar collector fields for district heat generation. This thesis concerns...