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Neural Network-based Approximation of Synthetic Market Generators
Get PDFIn this PhD thesis, we investigate the application of neural networks for simulating daily spot and equity European option markets to facilitate the automation of hedging a portfolio of derivatives by reinforcement learning algorithms such as Deep Hedging. The simulation of such markets poses several challenges: handling of high-dimensional option data, no-arbitrage constraints and estimating the market's transition dynamic from limited real-world datasets.
Among these challenges, we first focus on maintaining the arbitrage-free constraints in the generated call prices. Though arbitrage opportunities exist on the equities market, they are spurious, fleeting and often non-tradeable due to market frictions such as liquidity constraints and transaction costs. Furthermore, any arbitrage opportunity would be completely exploited by a downstream algorithm, making the approximated hedging strategy useless in practice. To ensure the absence of arbitrage in the generated call prices, we leverage an arbitrage-free parameterization through Discrete Local Volatilities. This parameterization simplifies the no arbitrage constraints of European call options to a positivity requirement and facilitates an efficient conversion to the original price space through a large-step implicit finite difference scheme.
Options are observed at various strikes and maturities and create an extremely high-dimensional space, making it particularly challenging to calibrate a conditional density that models the transition dynamic from the current to the next day's state due to the curse of dimensionality. We address this by using autoencoders that compress equivalent arbitrage-free option representation, the Discrete Local Volatility lattice, to an efficient low-dimensional non-linear embedding. This embedding, combined with the spot return is then used to define the market state from which we estimate transition dynamics.
Having obtained a low-dimensional arbitrage-free compressed representation, we next develop a model to estimate the conditional dynamic under the real-world measure for a single asset. For this purpose we introduce the neural spline flow - a highly versatile model defined by a collection of conditional cumulative distribution functions that characterize the conditional joint distribution through a neural network-based spline construction. We further extend the neural spline flow using path signatures from rough path theory and establish theoretical foundations that demonstrate practical advantages such as convexity in the model's parameters during calibration, mitigating the presence of local minima in the optimization function.
Since real-world hedging applications involve portfolios consisting of multiple underlyings or more complex options (such as basket, rainbow or spread options), we consider constructing a multi-asset market simulator. To address scalability challenges, we propose static and dynamic Gaussian copulas that are conditional on the market state to correlate already calibrated single-asset market simulators.
While we ensure in our real-world simulator that the spot process is a martingale and the call prices do not admit static arbitrage, the real-world simulator still admits statistical arbitrage, that is arbitrage in expectation, which is a weaker form of arbitrage. For this purpose, we propose to approximate a network-based measure change to obtain an approximation of the minimal entropy martingale measure - that is the martingale measure that is minimal with respect to the Kullback-Leibler divergence. Using the approximate near-martingale measure, we calibrate a new market simulator, that as evidenced through numerical findings, admits less statistical arbitrage.
All research presented in this thesis is accompanied by comprehensive numerical benchmarks that validate and demonstrate the effectiveness our approach.In dieser Dissertation untersuchen wir die Anwendung neuronaler Netzwerke für die Simulation von Aktien- und Optionsmärkten, um das automatisierte Hedging eines Derivateportfolios durch Reinforcement Learning Algorithmen wie Deep Hedging zu ermöglichen. Die Modellierung solcher Märkte stellt einige Herausforderungen: die Handhabung hochdimensionaler Optionsmärkte, Arbitragefreiheitsbedingungen in dem simulierten Preisprozess, und die Schätzung der Übergangsdynamik mit einer beschränkten Anzahl an Marktdaten.
Von diesen Herausforderungen widmen wir uns als erstes den Arbitragefreiheitsbedingungen in den generierten Europäischen Call-Preisen. Obwohl Arbitrage in Optionsmärkten existiert, sind die Möglichkeiten Arbitrage zu monetarisieren beschränkt durch Marktreibungen sowie Liquiditätsengpässe und Transaktionskosten. Um die Abwesenheit von statischen Arbitrage in den simulierten Call-Preisen zu garantieren, benutzen wir eine arbitragefreie Parametrisierung durch Diskrete Lokale Volatilitäten (DLV). Diese Parametrisierung vereinfacht die Arbitragefreiheitsbedingungen zu einer simplen Postivitätsbedingung in der generierten DLV und ermöglicht eine effiziente Konvertierung zurück zu den ursprünglichen Optionspreisen durch implizite Finite Differenzen, die nur an den Ablaufzeiten ermittelt werden muss.
Optionen werden am Markt für verschiedene Strikes und Ablaufzeiten gehandelt. Dies stellt ein extrem hochdimensionales Problem dar, welches es erschwert, nahezu unmöglich macht aufgrund des "Fluchs der Dimensionsalität", die Übergangsdynamik von einem zum nächsten Marktzustand zu schätzen. Um dies zu adressieren, benutzen wir Autoencoder um die äquivalente arbitragefreie Optionsparametrisierung, das DLV Gitter, zu einer niedrigdimensionalen nicht-linearen Einbettung zu komprimieren. Diese Einbettung wird dann in Kombination mit der Spot-Rendite den Markzustand definieren, aus dem wir die Übergangsdynamik schätzen.
Nach Erhalt der niedrigdimensionalen arbitragefreien Darstellung des Markts, widmen wir uns als nächstes dem Problem die bedingte Dynamik unter dem physischem Wahrscheinlichkeitsmaß zu schätzen. Dafür führen wir Neuronale Spline Flows (engl. neural spline flows) ein - ein äußerst flexibles Modell, welches aus einer Kollektion an bedingten kumulativen Verteilungsfunktionen besteht die durch neuronal Netz-basierte Splines parametrisiert wird. Des Weiteren erweitern wir die neuronalen Spline Flows durch Pfad Signaturen aus der Rauen Pfad Theorie (engl. rough path theory) und leiten theoretische Resultate her welche einige praktische Vorteile haben, sowie die Konvexität in der Kalibrierung der Modellparameter.
Realere Hedging Anwendungen betrachten in der Praxis Portfolios die aus mehreren Basiswerte und komplexere Optionen (sowie Basket-, Rainbow- und Spread-Optionen) bestehen. Aus diesem Grund betrachten wir die Konstruktion einen Multi-Asset Marktsimulators. Um Herausforderungen in der Skalierbarkeit eines solchen Simulators zu bewältigen, schlagen wir statische sowie dynamische Gauß'sche Kopulas vor, die vom Marktzustand abhängig sind. Die Kopulas werden dann benutzt um Marksimulatoren die auf Einzelwerten kalibriert wurden zu korrelieren.
Während wir in unserem Marktsimulator unter sicherstellen, dass der Spot-Prozess ein Martingal ist und die generierten Call-Preise keine statische Arbitrage zulassen, besitzt der Simulator dennoch statistische Arbitrage, das ist Arbitrage im Erwartungswert; eine schwächere Form von Arbitrage, die keinen Gewinn garantiert, doch im Mittel profitable ist. Um dieses Problem zu bewältigen, schlagen wir einen Maßwechsel vor, der durch ein neuronales Netzwerk kalibriert wird. Das erhaltene Maß ist eine Approximation vom minimalen Entropie-Martingalemaß, das ist das Martingalmaß, das bezüglich der Kullback-Leibler Divergenz dem physischem Maß am nächsten ist. Unter diesem "quasi"-Martingalmaß approximieren wir dann einen Marktsimulator der nachweislich weniger statistische Arbitragemöglichkeiten zulässt
Matrix Completion Methods for the Prediction of Thermodynamic Properties of Mixtures
Get PDFThe accurate prediction of thermodynamic properties is pivotal for chemical engineering as experimental data are scarce. While established physics-based methods face limitations in prediction accuracy and scope, emerging machine learning approaches, such as matrix completion methods (MCMs), offer promising alternatives. MCMs exploit the fact that experimental data for binary mixtures can be represented as elements of a sparse matrix, with rows and columns corresponding to the components that make up the mixture. Hence, MCMs can be used for closing the gaps in these matrices. In the present thesis, new methods for predicting thermodynamic properties of mixtures are developed that combine probabilistic MCMs with established physical methods. The resulting hybrid methods yield significantly improved predictions for key properties of binary mixtures, such as Henry’s law constants, activity coefficients at infinite dilution, and diffusion coefficients at infinite dilution, even when only limited experimental training data are available. In addition to predicting mixture properties directly, this thesis demonstrates that MCMs can also be applied to the pair-interaction parameters of physical group-contribution (GC) methods, which suffer from incomplete and improvable parameter sets limiting their applicability and accuracy. By using MCMs to infer the pair-interaction parameters, a comprehensive and consistent parameter set can be generated. This approach extends the applicability of widely used GC methods such as UNIFAC and modified UNIFAC (Dortmund), ultimately increasing their scope, predictive power, and robustness.Eine präzise Vorhersage thermodynamischer Eigenschaften ist in der chemischen Industrie von zentraler Bedeutung, da experimentelle Daten nur in begrenztem Umfang verfügbar sind. Während etablierte physikalische Methoden hinsichtlich Vorhersagegenauigkeit und Anwendungsbreite an ihre Grenzen stoßen, bieten neue Ansätze des maschinellen Lernens, insbesondere sogenannte Matrixvervollständigungsmethoden (Matrix Completion Methods, MCMs), vielversprechende Alternativen. MCMs schließen vorhandene Datenlücken, indem sie ausnutzen, dass experimentelle Daten für binäre Mischungen als Elemente einer spärlich besetzten Matrix dargestellt werden können, deren Zeilen und Spalten den Komponenten der Mischungen entsprechen. In der vorliegenden Dissertation werden neue Methoden zur Vorhersage thermodynamischer Eigenschaften von Mischungen entwickelt, die probabilistische MCMs mit etablierten physikalischen Methoden kombinieren. Diese hybriden Ansätze erzielen selbst bei geringer Verfügbarkeit experimenteller Trainingsdaten hohe Vorhersagegenauigkeiten für wichtige Eigenschaften binärer Mischungen wie Henry-Konstanten, Aktivitätskoeffizienten bei unendlicher Verdünnung und Diffusionskoeffizienten bei unendlicher Verdünnung. Neben der direkten Vorhersage von Mischungseigenschaften zeigt diese Dissertation, dass MCMs auch zur Parametrisierung von Gruppenbeitragsmethoden (GC-Methoden) verwendet werden können, die durch unvollständige Parametersätze eingeschränkt sind. Durch den Einsatz von MCMs zur Ermittlung der Paarwechselwirkungsparameter kann ein vollständiger und konsistenter Parametersatz erzeugt werden. Dieser Ansatz erweitert den Anwendungsbereich weit verbreiteter GC-Methoden wie UNIFAC und modified UNIFAC (Dortmund) und erhöht zusätzlich ihre Vorhersagegenauigkeit und Robustheit
Towards scan-to-BIM automation
Get PDFAs Building Information Modelling (BIM) continues to gain widespread adoption in the industry, its application in existing building works becomes increasingly relevant. To effectively apply BIM in alteration, renovation, and demolition projects, a model of the existing structure is crucial. While traditional methods relied on manual measurements and conventional surveying equipment, modern advancements have introduced efficient reality-capturing devices that combine Terrestrial Laser Scanners (TLS) and Structure from Motion (SfM) to rapidly acquire 3D data of entire buildings. However, the point clouds generated by these devices represent buildings as a dense collection of points, each covering physical objects with millions of data points. Since point clouds are unstructured data, they do not provide any further information about the building. Hence, it is essential to convert this data into Building Information Models (BIMs). Manually performing this conversion requires substantial effort, making the automation of the scan-to-BIM process critical for integrating existing structures into BIM workflows.
This work proposes a methodology for automatically generating BIMs from point clouds. The ScaleBIM framework consists of three main steps: (i) Semantic segmentation, where each point in the point cloud is assigned a semantic label, typically corresponding to a building element class. (ii) Geometry reconstruction, utilizing topology-aware refinement procedures to ensure the creation of a watertight BIM model that is functional for other use cases. (iii) Delivering the model in an open data format using open-source BIM authoring tools to maximize interoperability. These three steps are integrated into a comprehensive pipeline and rigorously tested on two datasets with varying characteristics. The pipeline reconstructs walls, doors and columns and delivers the respective BIM objects including the building component class and geometric shape representation.
Since the semantic segmentation procedure involves machine learning, annotated training data is necessary. To address this need, this work provides annotation guidelines and semiautomated annotation
procedures, along with two datasets comprising 2.8 billion annotated points and manually created reference BIMs. Additionally, efficient and robust filtering, downsampling and geometry reconstruction techniques have been either extended or newly developed. For both geometry reconstruction and open BIM authoring, this work introduces algorithms and procedures, including the two Python modules pystruct3d and openbimxd. Along with pipeline integration and evaluation, new metrics have been developed to provide a more realistic quantification of reconstruction accuracy. Finally, concluding remarks
highlight perspectives for future research
Efficient Adjoint-Based Design Capability for Unsteady Conjugate Heat Transfer Problems
Get PDFShape optimization using gradients computed via the adjoint method has become a common feature and also, practically, a requirement among the major computational fluid dynamics (CFD) and multi-physics solvers.
Accurate sensitivities are widespread available for single-zone steady-state problems, with unsteady or multi-physics adjoint solvers being less common.
Yet, gradient availability is a desirable feature for all primal simulation capabilities.
Many practical flows of industrial interest are unsteady in nature, and for the simulation of heating/cooling devices the coupling between a fluid and solid domain is essential to accurately capture the system's behavior.
Combining these two general observations of the demand for sensitivities and unsteady conjugate heat transfer applications, is the objective of the present work.
Consequently, this dissertation presents the development and application of an unsteady discrete adjoint solver for conjugate heat transfer (CHT).
Based on the framework available in the open-source multi-physics and design solver SU2, an efficient method to compute shape sensitivities via the discrete adjoint method for transient CHT problems is presented.
The handling of the algorithmic differentiation (AD) tool together with the orchestration of the numerous time-steps and various involved zones is crucial, to retain a code that is efficient with respect to memory and compute time. Therefore, a modular approach for the evaluation of the various derivative terms (diagonal, cross, dual-time-step) is used.
Beyond design for time-accurate simulations, capabilities for steady state optimization of repeating heat exchanger geometries, as pin-fin arrays, are developed.
For both tested CHT configurations (one unsteady and one steady), the gradient validation shows excellent accuracy against finite differences and successful constrained optimization highlights the practical applicability in a design chain.
The current development is not presented in isolation, but as a part of the SU2-project, for which detailed information is provided in the appropriate context
Amtliche Bekanntmachung der RPTU Kaiserslautern-Landau 2025.05
Get PDFAmtliche Bekanntmachung der RPTU Nr. 5/26.06.202
Zwischen Barriere und Ressource: Scham in der systemischen Beratung von Frauen mit Diskriminierungs- oder Belästigungserfahrung
Get PDFDie vorliegende Arbeit analysiert die Rolle, die Scham in der systemischen Beratung von diskriminierungs- und/oder belästigungsbetroffenen Frauen spielen kann, theoretisch und literaturbasiert. Es wird herausgestellt, welcher spezifischen Herangehensweisen es bedarf, um der Emotion und damit etwaig einhergehenden Hürden begegnen zu können. Des Weiteren wird überprüft, inwiefern die Bearbeitung und Berücksichtigung der Scham in Beratungen Potenziale freisetzt, um z. B. den Selbstwert und die Resilienz betroffener Personen stärken zu können. Dazu werden ausgewählte systemische Methoden auf ihre Eignung in diesen spezifischen Beratungssettings untersucht. Die Emotion der Scham wird in die Kontexte von Diskriminierungserfahrungen und systemischer Beratung von Frauen mit ebenjenen Erfahrungen gesetzt. Letztlich werden die angestellten theoretischen Überlegungen in Praxisempfehlungen für die systemische Arbeit überführt.
Die gewonnenen Erkenntnisse über eine gute Begleitung von Diskriminierungsbetroffenen dienen der Professionalisierung der systemischen Beratung im dargestellten Zusammenhang
Role of the chloroplast transporter ABCG7 in the acclimation of Arabidopsis to cold and freezing conditions
Get PDFAlthough ABCG7 protein levels decrease in the plastid proteome under cold conditions (Trentmann et al., 2020), the physiological role of the plastid ABC-type transporter ABCG7 during cold acclimation and freezing stress remains poorly understood and its localisation had not been experimentally confirmed. Employing transient expression of ABCG7-GFP in Nicotiana benthamiana and proteolytic assays in isolated chloroplasts, ABCG7 was shown to localise to the outer chloroplast envelope.
Characterisation of abcg7 loss-of-function mutants under cold stress revealed increased biomass accumulation, decreased glucose and starch levels, and elevated Krebs cycle intermediates. Metabolic changes were accompanied by increased anthocyanin synthesis and decreased phenylalanine levels, suggesting a shift of phenylalanine flux towards secondary metabolism, potentially contributing to enhanced cold tolerance. Further, a striking galactose accumulation was observed in abcg7 mutants during cold acclimation. When seedlings were grown on galactose supplemented plates, anthocyanin synthesis in abcg7 mutants was observed, and may explain the observed phenylalanine depletion.
Despite the cold tolerance, abcg7 mutants exhibited increased sensitivity to freezing. Expression and cell wall sugar analyses during post-freezing stress revealed altered cell wall composition, indicating cell wall fragility under sub-zero conditions. Freezing stress also triggered increased ABCG7 expression in wild types, suggesting a specific role in post-freezing recovery Figure 18C.
Given that plastid membranes are rich in galactolipids and highly vulnerable to freezing injury, the lipid composition and expression of membrane remodelling genes were analysed. In abcg7 mutants, lower levels of phosphor-, galacto- and storage lipids were detected during thawing, alongside with an altered expression pattern of the membrane remodelling enzyme SFR2. BiFC analysis confirmed a physical interaction between ABCG7 and SFR2, indicating a possible role for ABCG7 in the regulation of SFR2 activity and plastid membrane remodelling during freezing stress
Equivariant tropical cycles and moduli spaces of discrete admissible covers
Get PDFThis project originates in the divisor theory of discrete graphs and (abstract) tropical curves, and more precisely in their geometric gonality. The notion of geometric gonality concerns the degree of harmonic morphisms from tropical modifications of the source graph to a tree. We describe a tropical intersection theoretic framework that includes moduli spaces of tropical curves of positive genus (and possibly marked) motivated by a recent (at the time of the project) combinatorial proof of the following result: Every genus- graph has a tropical modification that is the source of a degree- tropical cover of a tree. The design of our framework not only furnishes a different proof of the previous result but also provides enough leeway for a systematic argument that generalizes the previous methods. In particular, after fixing the degree of the cover, the marking and genus of the target, and the ramification profiles above the marked ends we are able to study the loci of marked tropical curves that are the source of a tropical cover with these conditions. We arrive at these loci in two steps: first, we produce a tropical cycle in the corresponding moduli space of discrete admissible covers, then we pushforward this cycle through the corresponding source and forgetting-the-marking morphisms. Moreover, the first-mentioned result is just a consequence of the irreducibility of these moduli spaces (in a precise sense) and the special case of , , and . Our framework does not only shed new light into the underlying structure of these loci, and their general behavior, but also provides immediate access to some enumerative computations concerning these cycles, giving new proofs and generalizations of known results
Physical Layer Security in LEO Satellite Communication Systems - The Two Faces of Broadcasting and Mobility
Get PDFIn the last decade the field of satellite communication systems has experienced a golden age. Due to technological improvements the launch costs for satellites were reduced dramatically, so even private companies can launch their satellites. Today, large constellations of hundreds or thousands of satellites are launched into the low earth orbit (LEO). The internationally operating networks have the potential to connect users in the most remote areas. Thereby, the systems provide a wide variety of services, such as low data rate IoT communication, high throughput broadband access, and mobile connectivity.
This dissertation provides an introduction to communication satellite systems in general and focuses on two properties of LEO communication satellites that are unique in their combination: The broadcasting of traffic and the predictable, continuous mobility of low earth orbit satellites. The combination of these properties has not received much attention in satellite security research in the past. We aim to fill this gap by analyzing the potential of those two key properties for new attack vectors and possible defense mechanisms.
To investigate the effect of those properties, we developed a receiver network to make distributed traffic measurements of LEO satellite systems possible. To support the international research in this field, the network is open source and low cost. Currently, our instance of the network consists of 12 receivers that are internationally distributed, with a focus on central Europe.
The possibility to receive broadcasted traffic of other satellite users in combination with predictable satellite spot beam movements leads to an attack vector threatening the location privacy of satellite users. This vector applies to
every communication satellite system with predictable spot beam alignment. By using our receiver network, we were able to demonstrate the feasibility of this attack in the real world.
On the other hand, the possibility to observe traffic with multiple receivers and the known positions of satellites in their orbits can be used as a defense mechanisms. As an example for this, we developed an authentication scheme that determines if the signal was send by a valid satellite
Entwicklung, Stand und Funktion der Jüdischen Erwachsenenbildung in Österreich
Get PDFDie Arbeit untersucht die Entwicklung, Funktionen und Herausforderungen der jüdischen Erwachsenenbildung in Österreich. Im Zentrum steht die Frage, wie sich diese Bildungslandschaft - insb. auch seit - 1945 formiert hat, welche Stärken und Schwächen sie heute aufweist und welche Chancen und Bedrohungen erkennbar sind. Die Analyse zeigt, dass sich die jüdische Erwachsenenbildung aus einer historischen Ausnahmesituation heraus neu erfinden musste und sich inzwischen zu einem vielfältigen Bildungsfeld entwickelt hat, das sowohl religiöse als auch säkulare, kulturelle und berufliche Bedürfnisse abdeckt. Besonders hervorzuheben ist die institutionelle Struktur: Mit dem Jüdischen Institut für Erwachsenenbildung (JIFE), dem Jüdischen Beruflichen Bildungszentrum (JBBZ) und dem Lehrhaus Innsbruck existieren drei zentrale Einrichtungen unter jüdischer Trägerschaft, die spezifische Bildungsangebote für eine vergleichsweise kleine Bevölkerungsgruppe bereitstellen. Ergänzt wird dieses Kernangebot durch Volkshochschulen mit jüdischen Schwerpunkten, Forschungseinrichtungen, Museen, Kulturvereine, Gedenkstätten und Kultusgemeinden, die ein nahezu flächendeckendes Weiterbildungsangebot ermöglichen. Als wesentliche Bedrohung wird der zunehmende Antisemitismus identifiziert, der sowohl gesellschaftliche als auch sicherheitsrelevante Herausforderungen für jüdische Bildungseinrichtungen darstellt. Die politische und gesellschaftliche Auseinandersetzung mit diesem Phänomen bleibt daher zentral. Im Vergleich zu anderen religiösen Bildungsträgern zeigt sich, dass jüdisch-säkulare Erwachsenenbildung eine besondere thematische Ausrichtung auf Judentum, Israel und jüdische Identität aufweist, die in der nichtjüdischen säkularen Erwachsenenbildung kaum Entsprechungen findet. Die didaktische Analyse ergibt jedoch, dass keine spezifische „jüdische Didaktik“ erkennbar ist; vielmehr prägen thematische Schwerpunkte und institutionelle Vielfalt das Profil der jüdischen Erwachsenenbildung in Österreich