A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

The Legendre Formula in Clifford Analysis

2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.

On the Asymptotic Distribution of Closed Orbits for a Class of Open Billiards

2000 Mathematics Subject Classification: 37D40.

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

An asymptotic test for the Conditional Value-at-Risk

Conditional Value-at-Risk (equivalent to the Expected Shortfall, Tail Value-at-Risk and Tail Conditional Expectation in the case of continuous probability distributions) is an increasingly popular risk measure in the fields of actuarial science, banking and finance, and arguably a more suitable alternative to the currently widespread Value-at-Risk. In my paper, I present a brief literature survey, and propose a statistical test of the location of the CVaR, which may be applied by practising actuaries to test whether CVaR-based capital levels are in line with observed data. Finally, I conclude with numerical experiments and some questions for future research.

Corporate cash-pool valuation in a multi-firm context: a closed formula

Following our earlier paper on the subject, we present a general closed formula to value the interest savings due to a multi-firm cash-pool system. Assuming normal distribution of the accounts the total savings can be expressed as the product of three independent factors representing the interest spread, the number and the correlation of the firms, and the time-dependent distribution of the cash accounts. We derive analytic results for two special processes one characterizing the initial build-up period and the other describing the mature period. The value gained in the stationary system can be thought of as the interest, paid at the net interest spread rate on the standard deviation of the account. We show that pooling has substantial value already in the transient period. In order to increase the practical relevance of our analysis we discuss possible extensions of our model and we show how real option pricing technics can be applied here.

Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes

The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties.

Geometry of Dirac Operators

Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M \hat{\mathcal{A}}(TM)\wedge \text{ch}(\mathcal{V}) \] where $\mathcal{V} =\text{Hom}_{\mathbb{C}l(TM)}(\slashed{\mathsf{S}},S)$. We prove the above statement with the means of the heat kernel of the heat semigroup $e^{-tD^2}$. The first outstanding result is the McKean-Singer theorem that describes the index in terms of the supertrace of the heat kernel. The trace of heat kernel is obtained from local geometric information. Moreover, if we use the asymptotic expansion of the kernel we will see that in the computation of the index only one term matters. The Berezin formula tells us that the supertrace is nothing but the coefficient of the Clifford top part, and at the end, Getzler calculus enables us to find the integral of these top parts in terms of characteristic classes.

Riprogettazione di mozzi ruota per una vettura di Formula SAE

Con questa tesi si vuole illustrare e riordinare il lavoro da me svolto sulla progettazione di mozzi ruota e di altri componenti ad esso associati, relativi alla vettura del team di Formula SAE dell’Università di Bologna. Dopo una prima fase di studio del particolare componente tesa a definire quali caratteristiche fossero richieste al fine di raggiungere gli obbiettivi, si è passati allo sviluppo del progetto con lo svolgimento di primi calcoli a mano, per definire in linea di massima le sollecitazioni, per poi affinare il dimensionamento con le simulazioni FEM. Il componente è stato infine realizzato in lega d'alluminio ad elevate prestazioni.

Realizzazione e messa a punto degli impianti di raffreddamento e lubrificazione per una vettura di Formula SAE tramite analisi termofluidodinamica e acquisizione di telemetria in pista

L’obiettivo di questa tesi è illustrare quali siano stati i metodi di studio e le soluzioni adottate per ottimizzare gli impianti di raffreddamento e lubrificazione della monoposto da competizione sviluppata dal team Unibo Motorsport, in preparazione alla stagione di gara 2016 della Formula SAE®. Inizialmente saranno analizzate le principali problematiche di entrambi gli impianti attraverso simulazioni CFD (Computational Fluid Dynamics) e dati telemetrici degli anni passati. In seguito, saranno mostrati i diversi procedimenti di progettazione e il completamento degli impianti unitamente ad una loro valutazione economica. Infine, per verificare l’effettivo successo delle operazioni svolte a bordo vettura, verranno mostrate acquisizioni telemetriche relative alle gare ed altre simulazioni relative alle nuove geometrie sviluppate. Un altro obiettivo della trattazione è mettere a disposizione dei futuri membri del reparto motore un documento che contenga tutte le considerazioni fatte a riguardo degli impianti studiati. Questo è fondamentale all’interno di un ambiente come un team di Formula SAE®, dove ogni anno si ha il ricambio di una buona parte dei membri. Se gli studi svolti sugli impianti venissero persi, i nuovi arrivati si troverebbero a mettere le mani su un qualcosa di sconosciuto e lo sviluppo della vettura negli anni si troverebbe enormemente rallentato. Il “learning by doing” che ha sempre caratterizzato questo progetto viene infatti affiancato con armonia dalla possibilità di consultare esperienze pregresse relative al caso di studio considerato.