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.

From 3,3,4,4-Tetraethoxybut-1-yne to furan derivatives

The starting material for this project was the highly functionalized compound 3,3,4,4- tetraethoxybut-1-yne (TEB) and it can be prepared from ethyl vinyl ether by a 4-steps synthesis. The third and the fourth step in TEB synthesis were sensitive to reaction conditions, so it was developed a strategy to try to optimize the third step and obtain TEB with higher yields. An approach, which tries to optimize also the fourth step, will be developed in further works. Several γ-hydroxy-α,β-unsaturated acetylenic ketones can be prepared from 3,3,4,4- tetraethoxybut-1-yne. TEB and γ-hydroxy-α,β-unsaturated acetylenic ketones have been previously synthesized in good yields using various reaction routes. In this work will be shown the synthesis of 1,1-diethoxy-5-hydroxyhex-3-yn-2-one, 1,1-diethoxy-5-hydroxyundec-3-yn-2-one and 1,1-diethoxy-5-hydroxydodec-3-yn-2-one, which will react with ethyl acetoacetate to give, respectively, ethyl 4-(3,3-diethoxy-2-oxopropyl)-2,5-dimethylfuran-3-carboxylate, ethyl 4-(3,3-diethoxy-2-oxopropyl)-5-hexyl-2-methylfuran-3-carboxylate and ethyl 4-(3,3-diethoxy-2-oxopropyl)- 5-heptyl-2-methylfuran-3-carboxylate furan derivatives. This thesis project was carried out during the year 2011, at the Department of Chemistry of the University of Bergen.

Thermal inflation and the cosmological moduli problem

Ho studiato la possibilità di soluzione per il problema cosmologico dei moduli (CMP) presente a causa della compattificazione delle dimensioni extra tramite un periodo di inflazione a basse energie (Thermal Inflation). L'elaborato consta di cinque capitoli. Il primo introduce il lettore alla problematica dei moduli partendo dalla teoria Kaluza-Klein. Il secondo riguarda interamente il CMP e altri problemi cosmologici associati ai moduli. Nel terzo viene descritta la thermal inflation e le condizioni di funzionamento. Nel quarto capitolo viene preso in esame il problema di stabilizzazione dei moduli nella teoria di stringa tipo IIB: vengono descritti sia il meccanismo KKTL che il LVS. L'ultimo capitolo consiste nel calcolo della diluizione dei moduli, enunciata prima in un contesto generale e infine applicata al LVS, tramite la thermal inflation. Viene altresì presa in esame la possibilità di due epoche di thermal inflation, al fine di ottenere una diluizione più efficiente dei moduli. In LVS sono presenti due moduli, differenti per massa e vita media. Il più leggero è soggetto al CMP e si trova che, anche dopo due periodi di thermal inflation vi è ancora un numero eccessivo di tali campi, in quanto se da un lato la thermal inflation ne diliusca la densità iniziale, dall'altro ne causa una forte riproduzione, dovuta essenzialmente alle caratteristiche del modulo

Synthesis, reactivity and applications of 3,5-dimethyl-4-nitroisoxazole derivatives

3,5-dimethyl-4-nitroisoxazole derivatives are useful synthetic intermediates as the isoxazole nucleus chemically behaves as an ester, but establish better-defined interactions with chiral catalysts and lability of its N-O aromatic bond can unveil other groups such as 1,3-dicarbonyl compounds or carboxylic acids. In the present work, these features are employed in a 3,5-dimethyl-4-nitroisoxazole based synthesis of the γ-amino acid pregabalin, a medication for the treatment of epilepsy and neuropatic pain, in which this moiety is fundamental for the enantioselective formation of a chiral center by interaction with doubly-quaternized cinchona phase-transfer catalysts, whose ability of asymmetric induction will be investigated. Influence of this group in cinchona-derivatives catalysed stereoselective addition and Darzens reaction of a mono-chlorinated 3,5-dimethyl-4-nitroisoxazole and benzaldehyde will also be investigated.