Les marches aléatoires avec recherche de cible peuvent modéliser des réactions nucléaires ou la quête de nourriture par des animaux. Dans cette thèse, nous identifions des stratégies qui minimisent le temps moyen de première rencontre d’une cible (MFPT) pour plusieurs types de marches aléatoires. Premièrement, pour des marches symétriques ou avec biais, nous déterminons la distribution des temps de première sortie par une ouverture dans une paroi en forme de secteur angulaire, d’anneau ou de rectangle. Nous concluons sur la minimisation du MFPT en termes de la géométrie du confinement. Deuxièmement, pour des marches alternant entre diffusions volumique et surfacique, nous déterminons le temps moyen de première sortie par une ouverture dans la surface de confine- ment. Nous montrons qu’il existe un taux de désorption optimal qui minimise le MFPT. Nous justifions la généralité de l’optimalité par l’étude des rôles de la géométrie, de l’adsorption sur la surface et d’un biais en phase volumique. Troisièmement, pour des marches actives composées de phases balistiques entrecoupées par des réorientations aléatoires, nous obtenons l’expression du taux de réorientation qui minimise le MFPT en géométries sphériques de dimension deux ou trois. Dans un dernier chapitre, nous modélisons le mouvement de cellules eucaryotes par des marches browniennes actives. Nous expliquons pourquoi le temps de persistance évolue expo- nentiellement avec la vitesse de la cellule. Nous obtenons un diagramme des phases des types de trajectoires. Ce modèle minimal permet de quantifier l’efficacité des processus de recherche d’antigènes par des cellules immunitaires. / Random search processes can model nuclear reactions or animal foraging. In this thesis, we identify optimal search strategies which minimize the mean first passage time (MFPT) to a target for various processes. First, for symmetric and biased Brownian particles, we compute the distribution of exit times through an opening within the boundary of angular sectors, annuli and rectangles. We conclude on the optimizability of the MFPT in terms of geometric parameters. Second, for walks that switch between volume and surface diffusions, we determine the mean exit time through an opening inside the bounding surface. Under analytical criteria, an optimal desorption rate minimizes the MFPT. We justify that this optimality is a general property through a study of the roles of the geometry, of the adsorption properties and of a bias in the bulk random walk. Third, for active walks composed of straight runs interrupted by reorientations in a random direction, we obtain the expression of the optimal reorientation rate which minimizes the MFPT to a centered spherical target within a spherical confinement, in two and three dimensions. In a last chapter, we model the motion of eukaryotic cells by active Brownian walks. We explain an experimental observation: the persistence time is exponentially coupled with the speed of the cell. We also obtain a phase diagram for each type of trajectories. This model is a first step to quantify the search efficiency of immune cells in terms of a minimal number of biological parameters.

Contingent Convertibles (CoCos) are a new type of hybrid debt instrument characterized by forced equity conversion or write-down under a specified trigger event, usually indicating a state of near non-viability of the Additional Tier 1 capital category, giving them additional features such as possible coupon cancellation. In this thesis, the structure of CoCos is presented and different pricing approaches are introduced. A special focus is put on structural models with the Analytically Tractable First Passage Time(AT1P) Model and its extensions. Two models are applied on the write-down CoCo issued by Svenska Handelsbanken, starting with the equity derivative model and followed by the AT1P model. / Contingent Convertibles (Cocos) - villkorade konvertibla obligationer, är en ny typ av hybridinstrument som kännetecknas av konvertering till eget kapital eller nedskrivning av lånet vid en viss utlösande händelse, som vanligtvis indikerar ett tillstånd där den emitterande banken har behov av att absorbera förluster. Under strikta villkor kan dessa CoCo obligationer tillhöra primärkapital, där de kännetecknas av bland annat möjlig inställning av kuponger. I denna avhandling presenteras CoCons struktur och olika prissättningsmodeller läggs fram. Ett särskilt fokus läggs på strukturella modeller med “Analytically Tractable First Passage Time (AT1P) Model” och dess utvidgningar. Två modeller tillämpas på CoCon emitterad av Svenska Handelsbanken: “equity derivative” modellen och AT1P modellen.

Yes / The use of the Advanced Censored Closure (ACC) technique, recently proposed by the authors for predicting the peak response of linear structures vibrating under random processes, is extended to the case of non-linear oscillators driven by stationary white noise. The proposed approach requires the knowledge of mean upcrossing rate and spectral bandwidth of the response process, which in this paper are estimated through the Stochastic Averaging method. Numerical applications to oscillators with non-linear stiffness and damping are included, and the results are compared with those given by Monte Carlo Simulation and by other approximate formulations available in the literature.

In the thesis work we investigate four problems connected with dynamical processes in condensed medium, using different techniques of equilibrium and non-equilibrium statistical mechanics. Biology is rich in dynamical events ranging from processes involving single molecule [1] to collective phenomena [2]. In cell biology, translocation and transport processes of biological molecules constitute an important class of dynamical phenomena occurring in condensed phase. Examples include protein transport through membrane channels, gene transfer between bacteria, injection of DNA from virus head to the host cell, protein transport thorough the nuclear pores etc. We present a theoretical description of the problem of protein transport across the nuclear pore complex [3]. These nuclear pore complexes (NPCs) [4] are very selective filters that monitor the transport between the cytoplasm and the nucleoplasm. Two models have been suggested for the plug of the NPC. The first suggests that the plug is a reversible hydrogel while the other suggests that it is a polymer brush. In the thesis, we propose a model for the transport of a protein through the plug, which is treated as elastic continuum, which is general enough to cover both the models. The protein stretches the plug and creates a local deformation, which together with the protein is referred to as the bubble. The relevant coordinate describing the transport is the center of the bubble. We write down an expression for the energy of the system, which is used to analyze the motion. It shows that the bubble executes a random walk, within the gel. We find that for faster relaxation of the gel, the diffusion of the bubble is greater. Further, on adopting the same kind of free energy for the brush too, one finds that though the energy cost for the entry of the particle is small but the diffusion coefficient is much lower and hence, explanation of the rapid diffusion of the particle across the nuclear pore complex is easier within the gel model. In chemical physics, processes occurring in condensed phases like liquid or solid often involve barrier crossing. Simplest possible description of rate for such barrier crossing phenomena is given by the transition state theory [5]. One can go one step further by introducing the effect of the environment by incorporating phenomenological friction as is done in Kramer’s theory [6]. The “method of reactive flux” [7, 8] in chemical physics allows one to calculate the time dependent rate constant for a process involving large barrier by expressing the rate as an ensemble average of an infinite number of trajectories starting at the barrier top and ending on the product side at a specified later time. We compute the time dependent transmission coefficient using this method for a structureless particle surmounting a one dimensional inverted parabolic barrier. The work shows an elegant way of combining the traditional system plus reservoir model [9] and the method of reactive flux [7] and the normal mode analysis approach by Pollak [10] to calculate the time dependent transmission coefficient [11]. As expected our formula for the time dependent rate constant becomes equal to the transition state rate constant when one takes the zero time limit. Similarly Kramers rate constant is obtained by taking infinite time limit. Finally we conclude by noting that the method of analyzing the coupled Hamiltonian, introduced by Pollak is very powerful and it enables us to obtain analytical expressions for the time dependent reaction rate in case of Ohmic dissipation, even in underdamped case. The theory of first passage time [12] is one of the most important topics of research in chemical physics. As a model problem we consider a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space we derive a very general expression of the survival probability and the first passage time distribution, irrespective of the statistical nature of the dynamics. Also using the prescription adopted elsewhere [13] we define a bound to the actual survival probability and an approximate first passage time distribution which are expressed in terms of the position-position, velocity-velocity and position-velocity variances. Knowledge of these variances enables one to compute the survival probability and consequently the first passage distribution function. We compute both the quantities for gaussian Markovian process and also for non-Markovian dynamics. Our analysis shows that the survival probability decays exponentially at the long time, irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant [14]. Although the field of equilibrium thermodynamics and equilibrium statistical mechanics are well explored, there existed almost no theory for systems arbitrarily far from equilibrium until the advent of fluctuation theorems (FTs)[15] in mid 90�s. In general, these fluctuation theorems have provided a general prescription on energy exchanges that take place between a system and its surroundings under general nonequilibrium conditions and explain how macroscopic irreversibility appears naturally in systems that obey time reversible microscopic dynamics. Based on a Hamiltonian description we present a rigorous derivation [16] of the transient state work fluctuation theorem and the Jarzynski equality [17] for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is valid for a general non-Ohmic bath.

Questa tesi è composta da 3 differenti lavori che ci confermano la prevedibilità degli extra rendimenti rispetto al mercato usando semplici strategie di portafoglio azionario utilizzabili sia dal semplice risparmiatore sia dall'investitore istituzionale. Nel primo capitolo è stata analizzata la profittabilità della contrarian strategy nel mercato azionario Italiano. In letteratura é stato già abbondantemente dimostrato che i rendimenti azionari sono caratterizzati da un’autocorrelazione negativa nel breve periodo e da un effetto di ritorno alla media nel lungo periodo. La contrarian strategy é utilizzata per trarre profitto dalla correlazione seriale negativa dei rendimenti azionari, infatti, vendendo i titoli che si sono rivelati vincenti nel passato (in termini di rendimento) e acquistando quelli "perdenti" si ottengono profitti inaspettati. Nel secondo paper, l'analisi si focalizza sulla strategia di portafoglio definita Dollar Cost Averaging (DCA). La Dollar Cost Averaging si riferisce a una semplice metodologia di portafoglio che prevede di investire una somma fissa di denaro in un'attività rischiosa a uguali intervalli di tempo, per tutto l'orizzonte temporale prefissato. Il lavoro si propone di confrontare i vantaggi, in termini di riduzione sostanziale del rischio, di questa strategia dal punto di vista di un semplice risparmiatore. Nell'ultimo capitolo, ipotizzando di essere un investitore istituzionale che possiede ogni giorno numerose informazioni e previsioni, ho cercato di capire come egli può usare tutte le informazioni in suo possesso per decidere prontamente come allocare al meglio il patrimonio del fondo. L’investitore normalmente cerca di identificare la migliore previsione possibile, ma quasi sempre non riesce ad identificare l’esatto processo dei prezzi sottostanti. Quest’osservazione ha condotto molti ricercatori ad utilizzare numerosi fattori esplicativi per ottenere un buona previsione. Il paper supporta l’esistente letteratura che utilizza un nuovo approccio per trasformare previsioni di rendimenti in scelte di gestione di portafoglio che possano offrire una maggiore performance del portafoglio.Partendo dal modello d’incertezza di Pesaran e Timmerman(1996), considero un cospicuo numero di fattori macroeconomici per identificare un modello predittivo che mi permetta di prevedere i movimenti del mercato tenendo presente i maggiori indicatori economici e finanziari e considerato che il loro rispettivo potere predittivo cambia nel tempo. / This thesis is composed by three different papers that confirm us the predictability of expected returns using different simple portfolio strategy and under different point of view (i.e. a generic saver and institutional investor). In the first chapter, I investigate the profitability of contrarian strategy in the Italian Stock Market. However empirical research has shown that asset returns tend to exhibit some form of negative autocorrelation in the short term and mean-reversion over long horizons. Contrarian strategy is used to take advantage of serial correlation in stock price returns, such that selling winners and buying losers generates abnormal profits. On the second chapter, the analyse is focused in another classic portfolio strategy called Dollar Cost Averaging (DCA). Dollar Cost Averaging refers to an investment methodology in which a set dollar amount is invested in a risky asset at equal intervals over a holding period. The paper compares the advantages and risk of this strategy from the point of view of a saver. Lastly, supposing to be an institutional investor who has a large number of information and forecasts, I tried to understand how using all them he decide with dispatch how to allocate the portfolio fund. When a wide set of forecasts of some future economic events are available, decision makers usually attempt to discover which is the best forecast, but in almost all cases a decision maker cannot identify ex ante the true process. This observation has led researchers to introduce several sources of uncertainty in forecasting exercises. The paper supporting the existent literature employs a novel approaches to transform predicted returns into portfolio asset allocations, and their relative performances. First of all dealing with model uncertainty, as Pesaran and Timmerman (1996), I consider a richer parameterization for the forecasting model to find that the predictive power of various economic and financial factors over excess returns change through time.

No description available.

We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.

We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.

Single-particle tracking (SPT) is a method used to study the diffusion of various molecules within the cell. SPT involves tagging proteins with optical labels and observing their individual two-dimensional trajectories with a microscope. The analysis of this data provides important information about protein movement and mechanism, and is used to create multistate biological models. One of the challenges in SPT analysis is the variety of complex environments that contribute to heterogeneity within movement paths. In this thesis, we explore the limitations of current methods used to analyze molecular movement, and adapt analytical methods used in animal movement analysis, such as correlated random walks and first-passage time variance, to SPT data of leukocyte function-associated antigen-1 (LFA-1) integral membrane proteins. We discuss the consequences of these methods in understanding different types of heterogeneity in protein movement behaviour, and provide support to results from current experimental work. / Applied Mathematics

This dissertation presents a theoretical study of arbitrary discretizations of general nonequilibrium and non-steady-state systems. It will be shown that, without requiring the partitions of the phase-space to fulfill certain assumptions, such as culminating in Markovian partitions, a Markov chain can be constructed which has the same macro-change of probability of the occupation of the states as the original process. This is true for any classical and semiclassical system under any discrete or continuous, deterministic or stochastic, Markovian or non-Markovian dynamics. Restricted to classical and semi-classical systems, a formalism is developed which treats the projection of arbitrary (multidimensional) complex systems onto a discrete set of states of an abstract state-space using time and ensemble sampled transitions between the states of the trajectories of the original process. This formalism is then used to develop expressions for the mean first passage time and (in the case of projections resulting in pseudo-one-dimensional motion) for the individual residence times of the states using just the time and ensemble sampled transition rates. The theoretical work is illustrated by several numerical examples of non-linear diffusion processes. Those include the escape over a Kramers potential and a rough energy barrier, the escape from an entropic barrier, the folding process of a toy model of a linear polymer chain and the escape over a fluctuating barrier. The latter is an example of a non- Markovian dynamics of the original process. The results for the mean first passage time and the residence times (using both physically meaningful and non-meaningful partitions of the phase-space) confirms the theory. With an accuracy restricted only by the resolution of the measurement and/or the finite sampling size, the values of the mean first passage time of the projected process agree with those of a direct measurement on the original dynamics and with any available semi-analytical solution.