Jarrow-Yildirim model for inflation: theory and applications

This thesis deals with inflation theory, focussing on the model of Jarrow & Yildirim, which is nowadays used when pricing inflation derivatives. After recalling main results about short and forward interest rate models, the dynamics of the main components of the market are derived. Then the most important inflation-indexed derivatives are explained (zero coupon swap, year-on-year, cap and floor), and their pricing proceeding is shown step by step. Calibration is explained and performed with a common method and an heuristic and non standard one. The model is enriched with credit risk, too, which allows to take into account the possibility of bankrupt of the counterparty of a contract. In this context, the general method of pricing is derived, with the introduction of defaultable zero-coupon bonds, and the Monte Carlo method is treated in detailed and used to price a concrete example of contract. Appendixes: A: martingale measures, Girsanov's theorem and the change of numeraire. B: some aspects of the theory of Stochastic Differential Equations; in particular, the solution for linear EDSs, and the Feynman-Kac Theorem, which shows the connection between EDSs and Partial Differential Equations. C: some useful results about normal distribution.

Transportation theory and planning

The aim of this research is to analyze the transport system and its subcomponents in order to highlight which are the design tools for physical and/or organizational projects related to transport supply systems. A characteristic of the transport systems is that the change of their structures can recoil on several entities, groups of entities, which constitute the community. The construction of a new infrastructure can modify both the transport service characteristic for all the user of the entire network; for example, the construction of a transportation infrastructure can change not only the transport service characteristics for the users of the entire network in which it is part of, but also it produces economical, social, and environmental effects. Therefore, the interventions or the improvements choices must be performed using a rational decision making approach. This approach requires that these choices are taken through the quantitative evaluation of the different effects caused by the different intervention plans. This approach becomes even more necessary when the decisions are taken in behalf of the community. Then, in order to understand how to develop a planning process in Transportation I will firstly analyze the transport system and the mathematical models used to describe it: these models provide us significant indicators which can be used to evaluate the effects of possible interventions. In conclusion, I will move on the topics related to the transport planning, analyzing the planning process, and the variables that have to be considered to perform a feasibility analysis or to compare different alternatives. In conclusion I will perform a preliminary analysis of a new transit system which is planned to be developed in New York City.

Design and development of the new composite-material mainplane of the Dallara T12 race car

Abstract (US) Composite material components design and production techniques are discussed in the present graduation paper. In particular, this paper covers the design process and the production process of a carbon-fiber composite material component for a high performance car, more specifically, the Dallara T12 race car. This graduation paper is split in two. After a brief introduction on existing composite materials (their origins and applications), the first part of the present paper covers the main theoretical concepts behind the design of composite material components: particular focus will be given to carbon-fiber composites. The second part of the present paper covers the whole design and production process that the candidate carried out to create the new front mainplane of the Dallara T12 race car. This graduation paper is the result of a six-months-long internship that the candidate conducted as Design Office Trainee inside Dallara Automobili S.p.A. Abstract (ITA) La presente tesi di laurea discute le metodologie progettuali e produttive legate alla realizzazione di un componente in materiale composito. Nello specifico, viene discussa la progettazione e la produzione di un componente in fibra di carbonio destinato ad una vettura da competizione. La vettura in esame è la Dallara T12. Il lavoro è diviso in due parti. Nella prima parte, dopo una breve introduzione sull’origine e le tipologie di materiali compositi esistenti, vengono trattati i concetti teorici fondamentali su cui si basa la progettazione di generici componenti in materiale composito, con particolare riguardo ai materiali in fibra di carbonio. Nella seconda parte viene discusso tutto il processo produttivo che il candidato ha portato a termine per realizzare il nuovo alettone anteriore della Dallara T12. La presente tesi di laurea è il risultato del lavoro di progettazione che il candidato ha svolto presso l’Ufficio Tecnico di Dallara Automobili S.p.A. nel corso di un tirocinio formativo di sei mesi.

Planck stars: theory and phenomenology

General Relativity (GR) is one of the greatest scientific achievements of the 20th century along with quantum theory. Despite the elegance and the accordance with experimental tests, these two theories appear to be utterly incompatible at fundamental level. Black holes provide a perfect stage to point out these difficulties. Indeed, classical GR fails to describe Nature at small radii, because nothing prevents quantum mechanics from affecting the high curvature zone, and because classical GR becomes ill-defined at r = 0 anyway. Rovelli and Haggard have recently proposed a scenario where a negative quantum pressure at the Planck scales stops and reverts the gravitational collapse, leading to an effective “bounce” and explosion, thus resolving the central singularity. This scenario, called Black Hole Fireworks, has been proposed in a semiclassical framework. The purpose of this thesis is twofold: - Compute the bouncing time by means of a pure quantum computation based on Loop Quantum Gravity; - Extend the known theory to a more realistic scenario, in which the rotation is taken into account by means of the Newman-Janis Algorithm.