Uncertainty quantification for solar sails in the near-Earth environment

Solar sailing is a promising propellantless propulsion method that employs large reflective surfaces to harness solar radiation pressure for spacecraft propulsion. Despite the fact that several solar-sail near-Earth missions will launch in the coming years, there is notable lack of published studies on the uncertainties associated with missions...

An alternative approach to stochastic integration in Banach spaces

In his 2019 article, Kalinichenko proposed an alternative way of doing stochastic integration in general separable Banach spaces [12].This way circumvents the usual UMD assumption on our separable Banach space X, and instead imposes a strict condition on the integrating process $\Phi : (0,T)\times\Omega\to \Lll(H,X)$. Namely, we require the...

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...

A Novel Method for Solving High-Dimensional Backward Stochastic Differential Equations Using Malliavin Calculus and Deep Learning

Backward stochastic differential equations (BSDE) are known to be a powerful tool in mathematical modeling due to their inherent connection with second-order parabolic partial differential equations (PDE) established by the non-linear Feynman-Kac relations. The fundamental power of BSDEs lies in the fact that with them one does not merely obtain...

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...

Numerical Pricing of Equity Barrier Options with Local Volatility

This thesis is about the pricing of equity barrier options under local volatility. We study Dupire's nonparametric local volatility model, which can be defined in terms of call option prices or in terms of implied volatilities. No-arbitrage conditions are derived for the call option surface, and equivalent conditions for the total variance...

Controlled Distributions: An Analytical Approach to Stochastic Differential Equations

A literature study on controlled distributions, an analytical approach to stochastic differential equations.

Wind derivatives: Hedging wind risk

Wind derivatives are financial contracts that can be used to hedge or mitigate wind risk. In this thesis, the focus was on pricing these wind derivatives, incorporating a seasonality effect. A new method to incorporate seasonality is suggested, and various wind derivative pricing methods are provided.

A numerical method for backward stochastic differential equations with applications in finance.

This thesis starts by discussing the foundations of mathematical finance and some theoretical results on backward stochastic differential equations. We discuss some examples of these equations in mathematical finance (primarily option pricing) and develop a numerical method that can approximate solutions to these equations. Subsequently, we...