When to Cross the Spread: Curve Following with Singular Control

In this article the problem of curve following in an illiquid market is addressed. Using techniques of singular stochastic control, we extend the results of [NW11] to a twosided limit order market with temporary market impact and resilience, where the bid ask spread is now also controlled. We first show existence and uniqueness of an optimal control. In a second step, a suitable version of the stochastic maximum principle is derived which yields a characterisation of the optimal trading strategy in terms of a nonstandard coupled FBSDE. We show that the optimal control can be characterised via buy, sell and no-trade regions. The new feature is that we now get a nondegenerate no-trade region, which implies that market orders are only used when the spread is small. This allows to describe precisely when it is optimal to cross the bid ask spread, which is a fundamental problem of algorithmic trading. We also show that the controlled system can be described in terms of a reflected BSDE. As an application, we solve the portfolio liquidation problem with passive orders.Stochastic maximum principle, Convex analysis, Fully coupled forward backward stochastic differential equations, Trading in illiquid markets

Stochastic control in limit order markets

In dieser Dissertation lösen wir eine Klasse stochastischer Kontrollprobleme und konstruieren optimale Handelsstrategien in illiquiden Märkten. In Kapitel 1 betrachten wir einen Investor, der sein Portfolio nahe an einer stochastischen Zielfunktion halten möchte. Gesucht ist eine Strategie (aus aktiven und passiven Orders), die die Abweichung vom Zielportfolio und die Handelskosten minimiert. Wir zeigen Existenz und Eindeutigkeit einer optimalen Strategie. Wir beweisen eine Version des stochastischen Maximumprinzips und leiten damit ein Kriterium für Optimalität mittels einer gekoppelten FBSDE her. Wir beweisen eine zweite Charakterisierung mittels Kauf- und Verkaufregionen. Das Portfolioliquidierungsproblem wird explizit gelöst. In Kapitel 2 verallgemeinern wir die Klasse der zulässigen Strategien auf singuläre Marktorders. Wie zuvor zeigen wir Existenz und Eindeutigkeit einer optimalen Strategie. Im zweiten Schritt beweisen wir eine Version des Maximumprinzips im singulären Fall, die eine notwendige und hinreichende Optimalitätsbedingung liefert. Daraus leiten wir eine weitere Charakterisierung mittels Kauf-, Verkaufs- und Nichthandelsregionen ab. Wir zeigen, dass Marktorders nur benutzt werden, wenn der Spread klein genug ist. Wir schließen dieses Kapitel mit einer Fallstudie über Portfolioliquidierung ab. Das dritte Kapitel thematisiert Marktmanipulation in illiquiden Märkten. Wenn Transaktionen einen Einfluß auf den Aktienpreis haben, dann können Optionsbesitzer damit den Wert ihres Portfolios beeinflussen. Wir betrachten mehrere Agenten, die europäische Derivate halten und den Preis des zugrundeliegenden Wertpapiers beeinflussen. Wir beschränken uns auf risikoneutrale und CARA-Investoren und zeigen die Existenz eines eindeutigen Gleichgewichts, das wir mittels eines gekoppelten Systems nichtlinearer PDEs charakterisieren. Abschließend geben wir Bedingungen an, wie diese Art von Marktmanipulation verhindert werden kann.In this thesis we study a class of stochastic control problems and analyse optimal trading strategies in limit order markets. The first chapter addresses the problem of curve following. We consider an investor who wants to keep his stock holdings close to a stochastic target function. We construct the optimal strategy (comprising market and passive orders) which balances the penalty for deviating and the cost of trading. We first prove existence and uniqueness of an optimal control. The optimal trading strategy is then characterised in terms of the solution to a coupled FBSDE involving jumps via a stochastic maximum principle. We give a second characterisation in terms of buy and sell regions. The application of portfolio liquidation is studied in detail. In the second chapter, we extend our results to singular market orders using techniques of singular stochastic control. We first show existence and uniqueness of an optimal control. We then derive a version of the stochastic maximum principle which yields a characterisation of the optimal trading strategy in terms of a nonstandard coupled FBSDE. We show that the optimal control can be characterised via buy, sell and no-trade regions. We describe precisely when it is optimal to cross the bid ask spread. We also show that the controlled system can be described in terms of a reflected BSDE. As an application, we solve the portfolio liquidation problem with passive orders. When markets are illiquid, option holders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. In Chapter 3, we consider a model with competing players that hold European options and whose trading has an impact on the price of the underlying. We establish existence and uniqueness of equilibrium results and show that the equilibrium dynamics can be characterised in terms of a coupled system of non-linear PDEs. Finally, we show how market manipulation can be reduced

Validating Behavioral Requirements, Conditions, and Rules of Autonomous Systems with Scenario-Based Testing

Assuring the safety of autonomous vehicles is more and more approached by using scenario-based testing. Relevant driving situations are utilized here to fuel the argument that an autonomous vehicle behaves correctly. Many recent works focus on the specification, variation, generation, and execution of individual scenarios. However, it is still an open question if operational design domains, which describe the environmental conditions under which the system under test has to function, can be assessed with scenario-based testing. In this paper, we present open challenges and resulting research questions in the field of assuring the safety of autonomous vehicles. We have developed a toolchain that enables us to conduct scenario-based testing experiments based on scenario classification with temporal logic and driving data obtained from the CARLA simulator. We discuss the toolchain and present first results using analysis metrics like class coverage or distribution

Salinomycin as a Drug for Targeting Human Cancer Stem Cells

Cancer stem cells (CSCs) represent a subpopulation of tumor cells that possess self-renewal and tumor initiation capacity and the ability to give rise to the heterogenous lineages of malignant cells that comprise a tumor. CSCs possess multiple intrinsic mechanisms of resistance to chemotherapeutic drugs, novel tumor-targeted drugs, and radiation therapy, allowing them to survive standard cancer therapies and to initiate tumor recurrence and metastasis. Various molecular complexes and pathways that confer resistance and survival of CSCs, including expression of ATP-binding cassette (ABC) drug transporters, activation of the Wnt/β-catenin, Hedgehog, Notch and PI3K/Akt/mTOR signaling pathways, and acquisition of epithelial-mesenchymal transition (EMT), have been identified recently. Salinomycin, a polyether ionophore antibiotic isolated from Streptomyces albus, has been shown to kill CSCs in different types of human cancers, most likely by interfering with ABC drug transporters, the Wnt/β-catenin signaling pathway, and other CSC pathways. Promising results from preclinical trials in human xenograft mice and a few clinical pilote studies reveal that salinomycin is able to effectively eliminate CSCs and to induce partial clinical regression of heavily pretreated and therapy-resistant cancers. The ability of salinomycin to kill both CSCs and therapy-resistant cancer cells may define the compound as a novel and an effective anticancer drug

Illiquidity and Derivative Valuation

In illiquid markets, option traders may have an incentive to increase their portfolio value by using their impact on the dynamics of the underlying. We provide a mathematical framework within which to value derivatives under market impact in a multi-player framework by introducing strategic interactions into the model of Almgren and Chriss (2001). Specifically, we consider a financial market model with several strategically interacting players that hold European contingent claims and whose trading decisions have an impact on the price evolution of the underlying. We establish existence and uniqueness of equilibrium results for risk neutral and CARA investors and show that the equilibrium dynamics can be characterized in terms of a coupled system of possibly non-linear PDEs. For the linear cost function used in Almgren and Chriss (2001), we obtain a (semi) closed form solution. Analyzing this solution, we show how market manipulation can be reduced

Adaptive modification and flexibility of the proteasome system in response to proteasome inhibition

AbstractThe highly conserved ubiquitin–proteasome system is the principal machinery for extralysosomal protein degradation in eukaryotic cells. The 26S proteasome, a large multicatalytic multisubunit protease that processes cell proteins by limited and controlled proteolysis, constitutes the central proteolytic component of the ubiquitin–proteasome system. By processing cell proteins essential for development, differentiation, proliferation, cell cycling, apoptosis, gene transcription, signal transduction, senescence, and inflammatory and stress response, the 26S proteasome plays a key role in the regulation and maintenance of basic cellular processes. Various synthetic and biologic inhibitors with different inhibitory profiles towards the proteolytic activities of the 26S proteasome have been identified recently. Such proteasome inhibitors induce apoptosis and cell cycle arrest preferentially in neoplastic cells. Based on these findings proteasome inhibitors became useful in cancer therapy. However, under the pressure of continuous proteasome inhibition, eukaryotic cells can develop complex adaptive mechanisms to subvert the lethal attack of proteasome inhibitors. Such mechanisms include the adaptive modification of the proteasome system with increased expression, enhanced proteolytic activity and altered subcomplex assembly and subunit composition of proteasomes as well as the expression of a giant oligomeric protease complex, tripeptidyl peptidase II, which partially compensates for impaired proteasome function. Here we review the adaptive mechanisms developed by eukaryotic cells in response to proteasome inhibition. These mechanisms reveal enormous flexibility of the proteasome system and may have implications in cancer biology and therapy

Tracking a big anticyclonic eddy in the western Mediterranean Sea

12 pages, 10 figures, 1 table[EN] In May 1998 a big and deep open ocean anticyclonic eddy (AE 98-1) was sampled in the Algerian basin (western Mediterranean sea) in a region south of the Balearic islands. Fifteen surface Lagrangian buoys, tracked by satellite, were released across the eddy and were used for a few months to observe the continuity of the anticyclonic motion and the westward drift of the eddy. This kind of big and intense eddies in the Mediterranean can be detected by satellite altimeter radars. Using a new method, based on the Okubo-Weiss criterion, to identify mesoscale eddies in Sea Level Anomaly maps derived from measurements of the ERS and TOPEX/POSEIDON altimeters, an independent tracking of the same eddy was performed. There is a remarkable agreement between the two results despite the different nature of the information, mainly due to the fact that SLA maps contain interpolated and smoothed measurements while the drifter? trajectories are in situ data obtained from individual drifter fixes. The location of the eddy centre during two months with the two methods agrees within an average distance lower than the spatial resolution of the altimetric maps (0.2º). The size of the eddy, when it is possible to determine it, is also highly coincident in both cases (96.5% in diameter), and its average westwards translation speed is reasonably similar (24% lower from drifters). These results can be considered a good validation of the new tracking method in SLA maps in this specific case[ES] En mayo de 1998 un gran remolino anticiclónico de mar abierto fue observado al sur de las islas Baleares, en la cuenca Argelina (mar Mediterráneo occidental). Quince boyas superficiales de deriva fueron lanzadas a través del remolino, y su localización por satélite durante varios meses permitió seguir la continuidad del movimiento anticiclónico y el desplazamiento del remolino hacia el oeste. Este tipo de remolinos intensos puede ser detectado mediante radares altimétricos desde satélite. Un nuevo método, basado en el criterio de Okubo-Weiss, ha permitido seguir este mismo remolino en una serie de mapas de anomalías del nivel del mar obtenidos a partir de observaciones de los satélites ERS y TOPEX/POSEIDON. A pesar de que la información de los mapas altimétricos está interpolada y suavizada, y en cambio las trayectorias de los flotadores se han determinado a partir de localizaciones puntuales, se ha encontrado una concordancia notable entre ambos tipos de resultados. La posición del centro del remolino determinada con ambos métodos durante dos meses presenta unas diferencias que en promedio son menores que la resolución espacial de los mapas altimétricos (0.2º). El tamaño del remolino, cuando es posible calcularlo, es altamente coincidente (96.5% del diámetro), mientras que su velocidad de desplazamiento hacia el oeste es razonablemente parecida (24% inferior cuando se calcula a partir de los flotadores). Estos resultados pueden considerarse como una buena validación del nuevo método de seguimiento de remolinos de mesoescala en mapas altimétricos en el caso particular estudiadoThe ALGERS98 cruise on board the R/V Hespérides was part of the INTERMESO project funded by the Spanish National Programme on Environment and Natural Resources (AMB95-0901), and a contribution to the European research projects MATER (funded under contract MAS3-CT96-0051) and ALGERS (European Space Agency ERS AO E102/0)Peer reviewe

Untersuchungen zum Einfluss von 17 beta-Estradiol auf Gelenkknorpelgewebe unter proinflammatorischen Bedingungen in vitro

Osteoarthrose, eine Gelenkerkrankung in dessen Mittelpunkt die fortschreitende Zerstörung des Gelenkknorpels steht, erlebt aufgrund unserer alternden Gesellschaft eine steigende Inzidenz. Epidemiologische Untersuchungen zeigen die Besonderheit, dass postmenopausale Frauen besonders häufig unter Arthrose leiden, so dass man vermutet, die Knorpeldegeneration sei mit einem Mangel an Estradiol assoziiert. Experimente mit isolierten Knorpelzellen konnten den vermuteten protektiven Effekt des Estradiols überwiegend bestätigen, wohingegen Daten zu der Wirkung von Estradiol auf den Gewebeverband kaum vorliegen. In der vorliegenden Arbeit wird daher an einem in vitro Modell untersucht, welchen Einfluss Estradiol auf Knorpelexplantate unter proinflammatorischen Bedingungen ausübt