First-passage and escape problems in the Feller process

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.

Ruin and related quantities in some advanced insurance risk models

Risk theory has been a very active research area over the last decades. The main objectives of the theory are to find adequate stochastic processes which can model the surplus of a (non-life) insurance company and to analyze the risk related quantities such as ruin time, ruin probability, expected discounted penalty function and expected discounted dividend/tax payments. The study of these ruin related quantities provides crucial information for actuaries and decision makers. This thesis consists of the study of four different insurance risk models which are essentially related. The ruin and related quantities are investigated by using different techniques, resulting in explicit or asymptotic expressions for the ruin time, the ruin probability, the expected discounted penalty function and the expected discounted tax payments. - La recherche en théorie du risque a été très dynamique au cours des dernières décennies. D'un point de vue théorique, les principaux objectifs sont de trouver des processus stochastiques adéquats permettant de modéliser le surplus d'une compagnie d'assurance non vie et d'analyser les mesures de risque, notamment le temps de ruine, la probabilité de ruine, l'espérance de la valeur actuelle de la fonction de pénalité et l'espérance de la valeur actuelle des dividendes et taxes. L'étude de ces mesures associées à la ruine fournit des informations cruciales pour les actuaires et les décideurs. Cette thèse consiste en l'étude des quatre différents modèles de risque d'assurance qui sont essentiellement liés. La ruine et les mesures qui y sont associées sont examinées à l'aide de différentes techniques, ce qui permet d'induire des expressions explicites ou asymptotiques du temps de ruine, de la probabilité de ruine, de l'espérance de la valeur actuelle de la fonction de pénalité et l'espérance de la valeur actuelle des dividendes et taxes.

Statistical methods for river runoff prediction

Methods used to analyze one type of nonstationary stochastic processes?the periodically correlated process?are considered. Two methods of one-step-forward prediction of periodically correlated time series are examined. One-step-forward predictions made in accordance with an autoregression model and a model of an artificial neural network with one latent neuron layer and with an adaptation mechanism of network parameters in a moving time window were compared in terms of efficiency. The comparison showed that, in the case of prediction for one time step for time series of mean monthly water discharge, the simpler autoregression model is more efficient.

The IST METRA Project

This article summarizes the main achievementsof the Multi-Element Transmit andReceive Antennas (METRA) Project, an ISTresearch and technological development project carried out between January 2000 and June 2001 by Universitat Politècnica de Catalunya, the Center for Personkommunikation of Aalborg University, Nokia Networks, Nokia Mobile Phones, and Vodafone Group Research and Development.The main objective of METRA was the performanceevaluation of multi-antenna terminals incombination with adaptive antennas at the basestation in UMTS communication systems. 1 AMIMO channel sounder was developed that providedrealistic multi-antenna channel measurements.Using these measured data, stochasticchannel models were developed and properly validated.These models were also evaluated inorder to estimate their corresponding channelcapacity. Different MIMO configurations andprocessing schemes were developed for both theFDD and TDD modes of UTRA, and their linkperformance was assessed. Performance evaluationwas completed by system simulations thatillustrated the benefits of MIMO configurationsto the network operator. Implementation cost vs.performance improvement was also covered bythe project, including the base station and terminalmanufacturer and network operator viewpoints.Finally, significant standards contributionswere generated by the project and presented to the pertinent 3GPP working groups.

Frames: a maximum entropy statistical estimate of the inverse problem

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.

Stochasticity and bistability in horizontal transfer control of a genomic island in Pseudomonas.

Genomic islands (GEI) comprise a recently recognized large family of potentially mobile DNA elements and play an important role in the rapid differentiation and adaptation of bacteria. Most importantly, GEIs have been implicated in the acquisition of virulence factors, antibiotic resistances or toxic compound metabolism. Despite detailed information on coding capacities of GEIs, little is known about the regulatory decisions in individual cells controlling GEI transfer. Here, we show how self-transfer of ICEclc, a GEI in Pseudomonas knackmussii B13 is controlled by a series of stochastic processes, the result of which is that only a few percent of cells in a population will excise ICEclc and launch transfer. Stochastic processes have been implicated before in producing bistable phenotypic transitions, such as sporulation and competence development, but never before in horizontal gene transfer (HGT). Bistability is instigated during stationary phase at the level of expression of an activator protein InrR that lays encoded on ICEclc, and then faithfully propagated to a bistable expression of the IntB13 integrase, the enzyme responsible for excision and integration of the ICEclc. Our results demonstrate how GEI of a very widespread family are likely to control their transfer rates. Furthermore, they help to explain why HGT is typically confined to few members within a population of cells. The finding that, despite apparent stochasticity, HGT rates can be modulated by external environmental conditions provides an explanation as to why selective conditions can promote DNA exchange.

Renewal equations for option pricing

In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.

Langevin equations with multiplicative noise: Application to domain growth

Langevin Equations of Ginzburg-Landau form, with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hiliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical predictions of the linear analysis. We also present simulation results for spinodal decomposition at large times.

Coarse-graining and thermodynamics in far-from-equilibrium systems

Lying at the core of statistical physics is the need to reduce the number of degrees of freedom in a system. Coarse-graining is a frequently-used procedure to bridge molecular modeling with experiments. In equilibrium systems, this task can be readily performed; however in systems outside equilibrium, a possible lack of equilibration of the eliminated degrees of freedom may lead to incomplete or even misleading descriptions. Here, we present some examples showing how an improper coarse-graining procedure may result in linear approaches to nonlinear processes, miscalculations of activation rates and violations of the fluctuation-dissipation theorem.

First-passage and escape problems in the Feller process

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.

Ecuaciones de recurrencia estocásticas en el cálculo de la prima de reaseguro Finite Risk

RESUMEN: El objetivo de este trabajo es calcular el importe de la prima pura periódica que debe cobrar el reasegurador a la cedente en un reaseguro finite risk en ambiente financiero estocástico. El problema de la convolución de las diferentes variables aleatorias que intervienen en el cálculo de la prima lo hemos solucionado simulando, por Monte-Carlo, trayectorias de siniestralidad para el reasegurador aplicando posteriormente, en cada trayectoria simulada, los criterios de decisión financieros, esperanza, varianza y desviación. En los criterios de la varianza y de la desviación proponemos utilizar una ecuación de recurrencia estocástica para evitar el problema de la dependencia que existe entre los factores de capitalización estocásticos, obteniendo la prima de reaseguro en función del nivel de aversión al riesgo del reasegurador y de la volatilidad del tipo de interés. Palabras clave: Finite risk, ambiente estocástico, ecuación de recurrencia, simulación de Monte-Carlo, prima pura periódica.

Generalization transitions in Hidden-Layer neural networks for third-order feature discrimination

Stochastic learning processes for a specific feature detector are studied. This technique is applied to nonsmooth multilayer neural networks requested to perform a discrimination task of order 3 based on the ssT-block¿ssC-block problem. Our system proves to be capable of achieving perfect generalization, after presenting finite numbers of examples, by undergoing a phase transition. The corresponding annealed theory, which involves the Ising model under external field, shows good agreement with Monte Carlo simulations.

Local map update for large scale SLAM

A technique for simultaneous localisation and mapping (SLAM) for large scale scenarios is presented. This solution is based on the use of independent submaps of a limited size to map large areas. In addition, a global stochastic map, containing the links between adjacent submaps, is built. The information in both levels is corrected every time a loop is closed: local maps are updated with the information from overlapping maps, and the global stochastic map is optimised by means of constrained minimisation

Reaseguro Finite Risk en ambiente financiero estocástico

Una de las características del reaseguro finite risk es la existencia de una cuenta de experiencia, que está formada por las primas que cobra el reasegurador, junto con su rendimiento financiero,y su finalidad es financiar los siniestros que éste ha de satisfacer a la cedente en el plazo establecido. El objetivo de este trabajo es diseñar un modelo que permita determinar el saldo estimado o reserva que debe de tener en cada periodo anual la cuenta de experiencia para garantizar su solvencia dinámica, teniendo en cuenta la experiencia de siniestralidad de la cartera del reasegurador y de cada cedente. Para el cálculo de la prima de reaseguro y del saldo de la cuenta de experiencia se asumirá ambiente financiero estocástico, de modo que la prima de reaseguro dependerá también de otros parámetros como la volatilidad del tipo de interés o de la aversión al riesgo.

Multicointegration, polynomial cointegration and I(2) cointegration with structural breaks. An application to the sustainability of the US external deficit

In this paper we model the multicointegration relation, allowing for one structural break. Since multicointegration is a particular case of polynomial or I(2) cointegration, our proposal can also be applied in these cases. The paper proposes the use of a residualbased Dickey-Fuller class of statistic that accounts for one known or unknown structural break. Finite sample performance of the proposed statistic is investigated by using Monte Carlo simulations, which reveals that the statistic shows good properties in terms of empirical size and power. We complete the study with an empirical application of the sustainability of the US external deficit. Contrary to existing evidence, the consideration of one structural break leads to conclude in favour of the sustainability of the US external deficit.