Searched for: subject%3A%22Stochastic%255C+Differential%255C+Equations%22
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Garcia Bonilla, Juan (author)
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...
master thesis 2023
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de Graaff, Jan (author)
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...
master thesis 2022
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Liu, S. (author), Grzelak, L.A. (author), Oosterlee, C.W. (author)
We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By employing an artificial neural network to learn these...
journal article 2022
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van Rhijn, J. (author), Oosterlee, C.W. (author), Grzelak, L.A. (author), Liu, S. (author)
Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional Ito ^ stochastic differential equations (SDEs). We propose a scheme that approximates the path-wise conditional...
journal article 2022
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van Rhijn, J. (author)
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...
master thesis 2020
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Négyesi, Bálint (author)
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...
master thesis 2020
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de Boer, S.G. (author)
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...
master thesis 2020
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Goudsmit, L. (author)
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...
bachelor thesis 2020
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Blok, S.A.W. (author)
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...
bachelor thesis 2020
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Corstanje, Marc (author)
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...
master thesis 2019
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Burgers, Elsje (author)
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...
bachelor thesis 2018
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de Gijsel, Stefan (author)
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...
bachelor thesis 2018
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Frölke, Linde Josien (author)
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...
master thesis 2018
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van der Have, Z. (author), Oosterlee, C.W. (author)
In this paper, we consider the COS method for pricing European and Bermudan options under the stochastic alpha beta rho (SABR) model. In the COS pricing method, we make use of the characteristic function of the discrete forward process. We observe second-order convergence by using a second-order Taylor scheme in the discretization, or by...
journal article 2018
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Chau, K.W. (author), Oosterlee, C.W. (author)
We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based formula, resulting in an algorithm that is both accurate and easy to implement. Furthermore, we mitigate...
journal article 2018
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von Sydow, Lina (author), Milovanović, Slobodan (author), Larsson, Elisabeth (author), In 't Hout, Karel (author), Wiktorsson, Magnus (author), Oosterlee, C.W. (author), Shcherbakov, Victor (author), Wyns, Maarten (author), Leitao Rodriguez, A. (author), Jain, S. (author), Haentjens, Tinne (author), Waldén, Johan (author)
In the recent project BENCHOP–the BENCHmarking project in Option Pricing we found that Stochastic and Local Volatility problems were particularly challenging. Here we continue the effort by introducing a set of benchmark problems for this type of problems. Eight different methods targeted for the Stochastic Differential Equation (SDE)...
journal article 2018
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Ruijter, M.J. (author), Oosterlee, C.W. (author)
We develop a Fourier method to solve backward stochastic differential equations (BSDEs). A general theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier cosine series expansions, relying on the availability of a characteristic function. The method is...
journal article 2015
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Stout, M.I. (author)
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...
master thesis 2014
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Yan, D. (author)
A literature study on controlled distributions, an analytical approach to stochastic differential equations.
master thesis 2013
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Hoyer, S.A. (author)
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.
master thesis 2013
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