Central Clearing Valuation Adjustment

This paper develops an XVA (costs) analysis of centrally cleared trading, parallel to the one that has been developed in the last years for bilateral transactions. We introduce a dynamic framework that incorporates the sequence of cash-flows involved in the waterfall of resources of a clearing house. The total cost of the clearance framework for a clearing member, called CCVA for central clearing valuation adjustment, is decomposed into a CVA corresponding to the cost of its losses on the default fund in case of defaults of other member, an MVA corresponding to the cost of funding its margins and a KVA corresponding to the cost of the regulatory capital and also of the capital at risk that the member implicitly provides to the CCP through its default fund contribution. In the end the structure of the XVA equations for bilateral and cleared portfolios is similar, but the input data to these equations are not the same, reflecting different financial network structures. The resulting XVA numbers differ, but, interestingly enough, they become comparable after scaling by a suitable netting ratio

State Estimation for Distributed and Hybrid Systems

This thesis deals with two aspects of recursive state estimation: distributed estimation and estimation for hybrid systems. In the first part, an approximate distributed Kalman filter is developed. Nodes update their state estimates by linearly combining local measurements and estimates from their neighbors. This scheme allows nodes to save energy, thus prolonging their lifetime, compared to centralized information processing. The algorithm is evaluated experimentally as part of an ultrasound based positioning system. The first part also contains an example of a sensor-actuator network, where a mobile robot navigates using both local sensors and information from a sensor network. This system was implemented using a component-based framework. The second part develops, a recursive joint maximum a posteriori state estimation scheme for Markov jump linear systems. The estimation problem is reformulated as dynamic programming and then approximated using so called relaxed dynamic programming. This allows the otherwise exponential complexity to be kept at manageable levels. Approximate dynamic programming is also used to develop a sensor scheduling algorithm for linear systems. The algorithm produces an offline schedule that when used together with a Kalman filter minimizes the estimation error covariance

Multiscale derivation, analysis and simulation of collective dynamics models: geometrical aspects and applications

This thesis is a contribution to the study of swarming phenomena from the point of view of mathematical kinetic theory. This multiscale approach starts from stochastic individual based (or particle) models and aims at the derivation of partial differential equation models on statistical quantities when the number of particles tends to infinity. This latter class of models is better suited for mathematical analysis in order to reveal and explain large-scale emerging phenomena observed in various biological systems such as flocks of birds or swarms of bacteria. Within this objective, a large part of this thesis is dedicated to the study of a body-attitude coordination model and, through this example, of the influence of geometry on self-organisation. The first part of the thesis deals with the rigorous derivation of partial differential equation models from particle systems with mean-field interactions. After a review of the literature, in particular on the notion of propagation of chaos, a rigorous convergence result is proved for a large class of geometrically enriched piecewise deterministic particle models towards local BGK-type equations. In addition, the method developed is applied to the design and analysis of a new particle-based algorithm for sampling. This first part also addresses the question of the efficient simulation of particle systems using recent GPU routines. The second part of the thesis is devoted to kinetic and fluid models for body-oriented particles. The kinetic model is rigorously derived as the mean-field limit of a particle system. In the spatially homogeneous case, a phase transition phenomenon is investigated which discriminates, depending on the parameters of the model, between a “disordered” dynamics and a self-organised “ordered” dynamics. The fluid (or macroscopic) model was derived as the hydrodynamic limit of the kinetic model a few years ago by Degond et al. The analytical and numerical study of this model reveal the existence of new self-organised phenomena which are confirmed and quantified using particle simulations. Finally a generalisation of this model in arbitrary dimension is presented.Open Acces

Analysis of Embedded Controllers Subject to Computational Overruns

Microcontrollers have become an integral part of modern everyday embedded systems, such as smart bikes, cars, and drones. Typically, microcontrollers operate under real-time constraints, which require the timely execution of programs on the resource-constrained hardware. As embedded systems are becoming increasingly more complex, microcontrollers run the risk of violating their timing constraints, i.e., overrunning the program deadlines. Breaking these constraints can cause severe damage to both the embedded system and the humans interacting with the device. Therefore, it is crucial to analyse embedded systems properly to ensure that they do not pose any significant danger if the microcontroller overruns a few deadlines.However, there are very few tools available for assessing the safety and performance of embedded control systems when considering the implementation of the microcontroller. This thesis aims to fill this gap in the literature by presenting five papers on the analysis of embedded controllers subject to computational overruns. Details about the real-time operating system's implementation are included into the analysis, such as what happens to the controller's internal state representation when the timing constraints are violated. The contribution includes theoretical and computational tools for analysing the embedded system's stability, performance, and real-time properties.The embedded controller is analysed under three different types of timing violations: blackout events (when no control computation is completed during long periods), weakly-hard constraints (when the number of deadline overruns is constrained over a window), and stochastic overruns (when violations of timing constraints are governed by a probabilistic process). These scenarios are combined with different implementation policies to reduce the gap between the analysis and its practical applicability. The analyses are further validated with a comprehensive experimental campaign performed on both a set of physical processes and multiple simulations.In conclusion, the findings of this thesis reveal that the effect deadline overruns have on the embedded system heavily depends the implementation details and the system's dynamics. Additionally, the stability analysis of embedded controllers subject to deadline overruns is typically conservative, implying that additional insights can be gained by also analysing the system's performance

Analysis of DC microgrids as stochastic hybrid systems

A modeling framework for dc microgrids and distribution systems based on the dual active bridge (DAB) topology is presented. The purpose of this framework is to accurately characterize dynamic behavior of multi-converter systems as a function of exogenous load and source inputs. The base model is derived for deterministic inputs and then extended for the case of stochastic load behavior. At the core of the modeling framework is a large-signal DAB model that accurately describes the dynamics of both ac and dc state variables. This model addresses limitations of existing DAB converter models, which are not suitable for system-level analysis due to inaccuracy and poor upward scalability. The converter model acts as a fundamental building block in a general procedure for constructing models of multi-converter systems. System-level model construction is only possible due to structural properties of the converter model that mitigate prohibitive increases in size and complexity. To characterize the impact of randomness in practical loads, stochastic load descriptions are included in the deterministic dynamic model. The combined behavior of distributed loads is represented by a continuous-time stochastic process. Models that govern this load process are generated using a new modeling procedure, which builds incrementally from individual device-level representations. To merge the stochastic load process and deterministic dynamic models, the microgrid is modeled as a stochastic hybrid system. The stochastic hybrid model predicts the evolution of moments of dynamic state variables as a function of load model parameters. Moments of dynamic states provide useful approximations of typical system operating conditions over time. Applications of the deterministic models include system stability analysis and computationally efficient time-domain simulation. The stochastic hybrid models provide a framework for performance assessment and optimization --Abstract, page iv

CLADAG 2021 BOOK OF ABSTRACTS AND SHORT PAPERS

The book collects the short papers presented at the 13th Scientific Meeting of the Classification and Data Analysis Group (CLADAG) of the Italian Statistical Society (SIS). The meeting has been organized by the Department of Statistics, Computer Science and Applications of the University of Florence, under the auspices of the Italian Statistical Society and the International Federation of Classification Societies (IFCS). CLADAG is a member of the IFCS, a federation of national, regional, and linguistically-based classification societies. It is a non-profit, non-political scientific organization, whose aims are to further classification research