Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

Virtual Calibration of CO2 and Pollutant Emissions of a High-Performance PHEV using Model-in-the-Loop Methodology

The study analyses the calibration process of a newly developed high-performance plug-in hybrid electric passenger car powertrain. The complexity of modern powertrains and the more and more restrictive regulations regarding pollutant emissions are the primary challenges for the calibration of a vehicle’s powertrain. In addition, the managers of OEM need to know as earlier as possible if the vehicle under development will meet the target technical features (emission included). This leads to the necessity for advanced calibration methodologies, in order to keep the development of the powertrain robust, time and cost effective. The suggested solution is the virtual calibration, that allows the tuning of control functions of a powertrain before having it built. The aim of this study is to calibrate virtually the hybrid control unit functions in order to optimize the pollutant emissions and the fuel consumption. Starting from the model of the conventional vehicle, the powertrain is then hybridized and integrated with emissions and aftertreatments models. After its validation, the hybrid control unit strategies are optimized using the Model-in-the-Loop testing methodology. The calibration activities will proceed thanks to the implementation of a Hardware-in-the-Loop environment, that will allow to test and calibrate the Engine and Transmission control units effectively, besides in a time and cost saving manner.

A mathematical model of the early visual system and border completion via subriemannian Hamiltonian geodesics

In this thesis, we aim to discuss a simple mathematical model for the edge detection mechanism and the boundary completion problem in the human brain in a differential geometry framework. We describe the columnar structure of the primary visual cortex as the fiber bundle R2 × S1, the orientation bundle, and by introducing a first vector field on it, explain the edge detection process. Edges are detected through a lift from the domain in R2 into the manifold R2 × S1 and are horizontal to a completely non-integrable distribution. Therefore, we can construct a subriemannian structure on the manifold R2 × S1, through which we retrieve perceived smooth contours as subriemannian geodesics, solutions to Hamilton’s equations. To do so, in the first chapter, we illustrate the functioning of the most fundamental structures of the early visual system in the brain, from the retina to the primary visual cortex. We proceed with introducing the necessary concepts of differential and subriemannian geometry in chapters two and three. We finally implement our model in chapter four, where we conclude, comparing our results with the experimental findings of Heyes, Fields, and Hess on the existence of an association field.

On The Timing of Default Losses: When and Why?

At the light of what happened in 2010 and 2011, a lot of European countries founded themselves in a difficult position where all the credit rating agencies were downgrading debt states. Problem of solvency and guarantees on the states' bond were perceived as too risky for a Monetary Union as Europe is. Fear of a contagion from Greece as well was threatening the other countries as Italy, Spain, Portugal and Ireland; while Germany and France asked for a division between risky and riskless bond in order to feel more safe. Our paper gets inspiration by Roch and Uhlig (2011), it refers to the Argentinian case examined by Arellano (2008) and examine possible interventions as monetization or bailout as proposed by Cole and Kehoe (2000). We propose a model in which a state defaults and cannot repay a fraction of the old bond; but contrary to Roch and Uhlig that where considering a one-time cost of default we consider default as an accumulation of losses, perceived as unpaid fractions of the old debts. Our contributions to literature is that default immediately imply that economy faces a bad period and, accumulating losses, government will be worse-off. We studied a function for this accumulation of debt period by period, in order to get an idea of the magnitude of this waste of resources that economy will face when experiences a default. Our thesis is that bailouts just postpone the day of reckoning (Roch, Uhlig); so it's better to default before accumulate a lot of debts. What Europe need now is the introduction of new reforms in a controlled default where the Eurozone will be saved in its whole integrity and a state could fail with the future promise of a resurrection. As experience show us, governments are not interested into reducing debts since there are ECB interventions. That clearly create a distortion between countries in the same monetary union, giving to the states just an illusion about their future debtor position.

Adiabatic and local approximations for the kohn-sham potential in the hubbard model

We obtain the exact time-dependent Kohn-Sham potentials Vks for 1D Hubbard chains, driven by a d.c. external field, using the time-dependent electron density and current density obtained from exact many-body time-evolution. The exact Vxc is compared to the adiabatically-exact Vad-xc and the “instantaneous ground state” Vigs-xc. The effectiveness of these two approximations is analyzed. Approximations for the exchange-correlation potential Vxc and its gradient, based on the local density and on the local current density, are also considered and both physical quantities are observed to be far outside the reach of any possible local approximation. Insight into the respective roles of ground-state and excited-state correlation in the time-dependent system, as reflected in the potentials, is provided by the pair correlation function.

Development and application of a thermo-hydraulic model supporting the design and the deterministic safety analysis in a sodium cooled fast reactor

Il CP-ESFR è un progetto integrato di cooperazione europeo sui reattori a sodio SFR realizzato sotto il programma quadro EURATOM 7, che unisce il contributo di venticinque partner europei. Il CP-ESFR ha l'ambizione di contribuire all'istituzione di una "solida base scientifica e tecnica per il reattore veloce refrigerato a sodio, al fine di accelerare gli sviluppi pratici per la gestione sicura dei rifiuti radioattivi a lunga vita, per migliorare le prestazioni di sicurezza, l'efficienza delle risorse e il costo-efficacia di energia nucleare al fine di garantire un sistema solido e socialmente accettabile di protezione della popolazione e dell'ambiente contro gli effetti delle radiazioni ionizzanti. " La presente tesi di laurea è un contributo allo sviluppo di modelli e metodi, basati sull’uso di codici termo-idraulici di sistema, per l’ analisi di sicurezza di reattori di IV Generazione refrigerati a metallo liquido. L'attività è stata svolta nell'ambito del progetto FP-7 PELGRIMM ed in sinergia con l’Accordo di Programma MSE-ENEA(PAR-2013). Il progetto FP7 PELGRIMM ha come obbiettivo lo sviluppo di combustibili contenenti attinidi minori 1. attraverso lo studio di due diverse forme: pellet (oggetto della presente tesi) e spherepac 2. valutandone l’impatto sul progetto del reattore CP-ESFR. La tesi propone lo sviluppo di un modello termoidraulico di sistema dei circuiti primario e intermedio del reattore con il codice RELAP5-3D© (INL, US). Tale codice, qualificato per il licenziamento dei reattori nucleari ad acqua, è stato utilizzato per valutare come variano i parametri del core del reattore rilevanti per la sicurezza (es. temperatura di camicia e di centro combustibile, temperatura del fluido refrigerante, etc.), quando il combustibile venga impiegato per “bruciare” gli attinidi minori (isotopi radioattivi a lunga vita contenuti nelle scorie nucleari). Questo ha comportato, una fase di training sul codice, sui suoi modelli e sulle sue capacità. Successivamente, lo sviluppo della nodalizzazione dell’impianto CP-ESFR, la sua qualifica, e l’analisi dei risultati ottenuti al variare della configurazione del core, del bruciamento e del tipo di combustibile impiegato (i.e. diverso arricchimento di attinidi minori). Il testo è suddiviso in sei sezioni. La prima fornisce un’introduzione allo sviluppo tecnologico dei reattori veloci, evidenzia l’ambito in cui è stata svolta questa tesi e ne definisce obbiettivi e struttura. Nella seconda sezione, viene descritto l’impianto del CP-ESFR con attenzione alla configurazione del nocciolo e al sistema primario. La terza sezione introduce il codice di sistema termico-idraulico utilizzato per le analisi e il modello sviluppato per riprodurre l’impianto. Nella sezione quattro vengono descritti: i test e le verifiche effettuate per valutare le prestazioni del modello, la qualifica della nodalizzazione, i principali modelli e le correlazioni più rilevanti per la simulazione e le configurazioni del core considerate per l’analisi dei risultati. I risultati ottenuti relativamente ai parametri di sicurezza del nocciolo in condizioni di normale funzionamento e per un transitorio selezionato sono descritti nella quinta sezione. Infine, sono riportate le conclusioni dell’attività.

Laplace operator on finite graphs and a network diffusion model for the progression of the Alzheimer disease

Nella tesi viene descritto il Network Diffusion Model, ovvero il modello di A. Ray, A. Kuceyeski, M. Weiner inerente i meccanismi di progressione della demenza senile. In tale modello si approssima l'encefalo sano con una rete cerebrale (ovvero un grafo pesato), si identifica un generale fattore di malattia e se ne analizza la propagazione che avviene secondo meccanismi analoghi a quelli di un'infezione da prioni. La progressione del fattore di malattia e le conseguenze macroscopiche di tale processo(tra cui principalmente l'atrofia corticale) vengono, poi, descritte mediante approccio matematico. I risultati teoretici vengono confrontati con quanto osservato sperimentalmente in pazienti affetti da demenza senile. Nella tesi, inoltre, si fornisce una panoramica sui recenti studi inerenti i processi neurodegenerativi e si costruisce il contesto matematico di riferimento del modello preso in esame. Si presenta una panoramica sui grafi finiti, si introduce l'operatore di Laplace sui grafi e si forniscono stime dall'alto e dal basso per gli autovalori. Al fine di costruire una cornice matematica completa si analizza la relazione tra caso discreto e continuo: viene descritto l'operatore di Laplace-Beltrami sulle varietà riemanniane compatte e vengono fornite stime dall'alto per gli autovalori dell'operatore di Laplace-Beltrami associato a tali varietà a partire dalle stime dall'alto per gli autovalori del laplaciano sui grafi finiti.

Analytical model for the prediction of wrinkling of rear pressure bulkheads

In Airbus GmbH (Hamburg) has been developed a new design of Rear Pressure Bulkhead (RPB) for the A320-family. The new model has been formed with vacuum forming technology. During this process the wrinkling phenomenon occurs. In this thesis is described an analytical model for prediction of wrinkling based on the energetic method of Timoshenko. Large deflection theory has been used for analyze two cases of study: a simply supported circular thin plate stamped by a spherical punch and a simply supported circular thin plate formed with vacuum forming technique. If the edges are free to displace radially, thin plates will develop radial wrinkles near the edge at a central deflection approximately equal to four plate thicknesses w0/ℎ≈4 if they’re stamped by a spherical punch and w0/ℎ≈3 if they’re formed with vacuum forming technique. Initially, there are four symmetrical wrinkles, but the number increases if the central deflection is increased. By using experimental results, the “Snaptrhough” phenomenon is described.

Development of the Simulation Model for the CoSES Laboratory Test Microgrid in Modelica

Evolution of the traditional consumer in a power system to a prosumer has posed many problems in the traditional uni-directional grid. This evolution in the grid model has made it important to study the behaviour of microgrids. This thesis deals with the laboratory microgrid setup at the Munich School of Engineering, built to assist researchers in studying microgrids. The model is built in Dymola which is a tool for the OpenModelica language. Models for the different components were derived, suiting the purpose of this study. The equivalent parameters were derived from data sheets and other simulation programs such as PSCAD. The parameters were entered into the model grid and tested at steady state, firstly. This yielded satisfactory results that were similar to the reference results from MATPOWER power flow. Furthermore, fault conditions at several buses were simulated to observe the behaviour of the grid under these conditions. Recommendations for further developing this model to include more detailed models for components, such as power electronic converters, were made at the end of the thesis.

Diffusion model of the hollow electron lens for HL-LHC

In the upcoming years, various upgrades and improvements are planned for the CERN Large Hadron Collider (LHC) and represent the mandate of the High-Luminosity project. The upgrade will allow for a total stored beam energy of about 700 MJ, which will need, among others, an extremely efficient collimation system. This will be achieved with the addition of a hollow electron lens (HEL) system to help control the beam-halo depletion and mitigate the effects of fast beam losses. In this master thesis, we present a diffusion model of the HEL for HL-LHC. In particular, we explore several scenarios to use such a device, focusing on the halo depletion efficiency given by different noise regimes.

Integrating an Emotion Recognition Model for the Flobi System

This thesis investigates if emotional states of users interacting with a virtual robot can be recognized reliably and if specific interaction strategy can change the users’ emotional state and affect users’ risk decision. For this investigation, the OpenFace [1] emotion recognition model was intended to be integrated into the Flobi [2] system, to allow the agent to be aware of the current emotional state of the user and to react appropriately. There was an open source ROS [3] bridge available online to integrate OpenFace to the Flobi simulation but it was not consistent with some other projects in Flobi distribution. Then due to technical reasons DeepFace was selected. In a human-agent interaction, the system is compared to a system without using emotion recognition. Evaluation could happen at different levels: evaluation of emotion recognition model, evaluation of the interaction strategy, and evaluation of effect of interaction on user decision. The results showed that the happy emotion induction was 58% and fear emotion induction 77% successful. Risk decision results show that: in happy induction after interaction 16.6% of participants switched to a lower risk decision and 75% of them did not change their decision and the remaining switched to a higher risk decision. In fear inducted participants 33.3% decreased risk 66.6 % did not change their decision The emotion recognition accuracy was and had bias to. The sensitivity and specificity is calculated for each emotion class. The emotion recognition model classifies happy emotions as neutral in most of the time.

Crowd-shipping and autonomous vehicles: an optimization model for the last mile delivery

Il seguente elaborato propone un modello innovativo per la gestione della logistica distributiva nell’ultimo miglio, congiungendo l’attività di crowd-shipping con la presenza di Autonomous Vehicles, per il trasporto di prodotti all’interno della città. Il crowd-shipping utilizza conducenti occasionali, i quali deviano il loro tragitto in cambio di una ricompensa per il completamento dell’attività. Dall’altro lato, gli Autonomous Vehicles sono veicoli elettrici a guida autonoma, in grado di trasportare un numero limitato di pacchi e dotati di un sistema di sicurezza avanzato per garantire la fiducia nel trasporto. In primo luogo, nel seguente elaborato verrà mostrato il modello di ottimizzazione che congiunge i due attori principali in un unico ambiente, dove sono presenti un numero determinato di prodotti da muovere. Successivamente, poiché il problema di ottimizzazione è molto complesso e il numero di istanze valutabili è molto basso, verranno presentate due soluzioni differenti. La prima riguarda la metaeuristica chiamata Ant System, che cerca di avvicinarsi alle soluzioni ottime del precedente modello, mentre la seconda riguarda l’utilizzo di operatori di Local Search, i quali permettono di valutare soluzioni per istanze molto più grandi rispetto alla metaeuristica. Infine, i due modelli euristici verranno utilizzati per analizzare uno scenario che cerca di riprodurre una situazione reale. Tale scenario tenta di allocare strategicamente le risorse presenti e permette di dimostrare che gli Autonomous Vehicles riescono a supportare gli Occasional Drivers anche quando il numero di prodotti trasportabili è elevato. Inoltre, le due entità proposte riescono a soddisfare la domanda, garantendo un servizio che nel futuro potrebbe sostituire il tradizionale sistema di logistica distributiva last mile.