Mathematical control theory and Finance

Control theory provides a large set of theoretical and computational tools with applications in a wide range of fields, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to find solutions to ”real life” problems, as is the case in robotics, control of industrial processes or finance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the financial analyst to possess a high level of mathematical skills. Conversely, the complex challenges posed by the problems and models relevant to finance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical finance. Up to now, other branches of control theory have found comparatively less application in financial problems. To some extent, deterministic and stochastic control theories developed as different branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these fields has intensified. Some concepts from stochastic calculus (e.g., rough paths) have drawn the attention of the deterministic control theory community. Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic control. We strongly believe in the possibility of a fruitful collaboration between specialists of deterministic and stochastic control theory and specialists in finance, both from academic and business backgrounds. It is this kind of collaboration that the organizers of the Workshop on Mathematical Control Theory and Finance wished to foster. This volume collects a set of original papers based on plenary lectures and selected contributed talks presented at the Workshop. They cover a wide range of current research topics on the mathematics of control systems and applications to finance. They should appeal to all those who are interested in research at the junction of these three important fields as well as those who seek special topics within this scope.info:eu-repo/semantics/publishedVersio

Stochastic Processes And Their Applications To Change Point Detection Problems

This dissertation addresses the change point detection problem when either the post-change distribution has uncertainty or the post-change distribution is time inhomogeneous. In the case of post-change distribution uncertainty, attention is drawn to the construction of a family of composite stopping times. It is shown that the proposed composite stopping time has third order optimality in the detection problem with Wiener observations and also provides information to distinguish the different values of post-change drift. In the case of post-change distribution uncertainty, a computationally efficient decision rule with low-complexity based on Cumulative Sum (CUSUM) algorithm is also introduced. In the time inhomogeneous case where the post-change drift is a function of time, a two-stage stopping time that contains both CUSUM and sequential probability ratio test (SPRT) procedures is considered, whose expected values are given in explicit form. The two-stage stopping time can provide additional information when comparing with CUSUM stopping times. Moreover, the thesis also addresses the joint distribution of maximum drawdown and maximum drawup for any drifted Brownian motion killed at an independent exponentially distributed random time, and as its application, upper and lower bounds of expected time of the minimum between two correlated CUSUM stopping times are provided, where the correlation coefficient is present explicitly

Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields

This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners

DATA-DRIVEN REAL-TIME GEOSTEERING USING SURFACE DRILLING DATA

In this thesis I present a method for estimating lithology or deriving formation properties from real-time surface drilling data. This information can then be used to enhance real-time geosteering capabilities. Current approaches for geosteering often rely on data from an MWD sub. Because of the position of the MWD sub relative to the bit, the MWD sub is relating information that is depth- and time-delayed relative to the bit. In this work, I use a data-driven approach that relies on the use of Hidden Markov Models (HMM) and Change Point Detection (CPD) algorithms to relate surface drilling signals to formation properties/lithology. My approach views the surface drilling data as a multichannel time-series signal which is an advantage over prior approaches that have attempted to derive variations in lithology from surface drilling data. I finally test my approach with two field datasets: the first is the Volve Oilfield in offshore Norway, and the second is the Meramec formation in the Oklahoma STACK. In both case studies, I demonstrate that the use of HMM and/or CPD can substantially enhance resolution of lithology changes from surface drilling data alone and can therefore be a promising approach for use in real-time geosteering decisions

Directional Estimation for Robotic Beating Heart Surgery

In robotic beating heart surgery, a remote-controlled robot can be used to carry out the operation while automatically canceling out the heart motion. The surgeon controlling the robot is shown a stabilized view of the heart. First, we consider the use of directional statistics for estimation of the phase of the heartbeat. Second, we deal with reconstruction of a moving and deformable surface. Third, we address the question of obtaining a stabilized image of the heart

Text mining and natural language processing for the early stages of space mission design

Final thesis submitted December 2021 - degree awarded in 2022A considerable amount of data related to space mission design has been accumulated since artificial satellites started to venture into space in the 1950s. This data has today become an overwhelming volume of information, triggering a significant knowledge reuse bottleneck at the early stages of space mission design. Meanwhile, virtual assistants, text mining and Natural Language Processing techniques have become pervasive to our daily life. The work presented in this thesis is one of the first attempts to bridge the gap between the worlds of space systems engineering and text mining. Several novel models are thus developed and implemented here, targeting the structuring of accumulated data through an ontology, but also tasks commonly performed by systems engineers such as requirement management and heritage analysis. A first collection of documents related to space systems is gathered for the training of these methods. Eventually, this work aims to pave the way towards the development of a Design Engineering Assistant (DEA) for the early stages of space mission design. It is also hoped that this work will actively contribute to the integration of text mining and Natural Language Processing methods in the field of space mission design, enhancing current design processes.A considerable amount of data related to space mission design has been accumulated since artificial satellites started to venture into space in the 1950s. This data has today become an overwhelming volume of information, triggering a significant knowledge reuse bottleneck at the early stages of space mission design. Meanwhile, virtual assistants, text mining and Natural Language Processing techniques have become pervasive to our daily life. The work presented in this thesis is one of the first attempts to bridge the gap between the worlds of space systems engineering and text mining. Several novel models are thus developed and implemented here, targeting the structuring of accumulated data through an ontology, but also tasks commonly performed by systems engineers such as requirement management and heritage analysis. A first collection of documents related to space systems is gathered for the training of these methods. Eventually, this work aims to pave the way towards the development of a Design Engineering Assistant (DEA) for the early stages of space mission design. It is also hoped that this work will actively contribute to the integration of text mining and Natural Language Processing methods in the field of space mission design, enhancing current design processes

Directional Estimation for Robotic Beating Heart Surgery

In robotic beating heart surgery, a remote-controlled robot can be used to carry out the operation while automatically canceling out the heart motion. The surgeon controlling the robot is shown a stabilized view of the heart. First, we consider the use of directional statistics for estimation of the phase of the heartbeat. Second, we deal with reconstruction of a moving and deformable surface. Third, we address the question of obtaining a stabilized image of the heart