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.

Comparing N = 1 effect size indices in presence of autocorrelation

Generalization from single-case designs can be achieved by means of replicating individual studies across different experimental units and settings. When replications are available, their findings can be summarized using effect size measurements and integrated through meta-analyses. Several procedures are available for quantifying the magnitude of treatment"s effect in N = 1 designs and some of them are studied in the current paper. Monte Carlo simulations were employed to generate different data patterns (trend, level change, slope change). The experimental conditions simulated were defined by the degrees of serial dependence and phases" length. Out of all the effect size indices studied, the Percent of nonoverlapping data and standardized mean difference proved to be less affected by autocorrelation and perform better for shorter data series. The regression-based procedures proposed specifically for single-case designs did not differentiate between data patterns as well as simpler indices.

Randomization tests for ABAB designs: Comparing-data-division-specific and common distributions

Monte Carlo simulations were used to generate data for ABAB designs of different lengths. The points of change in phase are randomly determined before gathering behaviour measurements, which allows the use of a randomization test as an analytic technique. Data simulation and analysis can be based either on data-division-specific or on common distributions. Following one method or another affects the results obtained after the randomization test has been applied. Therefore, the goal of the study was to examine these effects in more detail. The discrepancies in these approaches are obvious when data with zero treatment effect are considered and such approaches have implications for statistical power studies. Data-division-specific distributions provide more detailed information about the performance of the statistical technique.

Monotonic continuous-time random walks with drift and stochastic reset events

In this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes. We focus our attention on monotonic continuous-time random walks with a constant drift: The process increases between the reset events, either by the effect of the random jumps, or by the action of the deterministic drift. As a result of all these combined factors interesting properties emerge, like the existence (for any drift strength) of a stationary transition probability density function, or the faculty of the model to reproduce power-law-like behavior. General formulas for two extreme statistics, the survival probability, and the mean exit time, are also derived. To corroborate in an independent way the results of the paper, Monte Carlo methods were used. These numerical estimations are in full agreement with the analytical predictions.

Radial dose function of a 90Sr 90Y seed in water and A150: Comment on Calibration and characterization of beta-particle sources for intravascular brachytherapy

Intravascular brachytherapy with beta sources has become a useful technique to prevent restenosis after cardiovascular intervention. In particular, the Beta-Cath high-dose-rate system, manufactured by Novoste Corporation, is a commercially available 90Sr 90Y source for intravascular brachytherapy that is achieving widespread use. Its dosimetric characterization has attracted considerable attention in recent years. Unfortunately, the short ranges of the emitted beta particles and the associated large dose gradients make experimental measurements particularly difficult. This circumstance has motivated the appearance of a number of papers addressing the characterization of this source by means of Monte Carlo simulation techniques.

Molecular dynamics simulation of the spherical electrical double layer of a soft nanoparticle. Effect of the surface and counterion valence

Molecular dynamics simulations were performed to study the ion and water distribution around a spherical charged nanoparticle. A soft nanoparticle model was designed using a set of hydrophobic interaction sites distributed in six concentric spherical layers. In order to simulate the effect of charged functionalyzed groups on the nanoparticle surface, a set of charged sites were distributed in the outer layer. Four charged nanoparticle models, from a surface charge value of −0.035 Cm−2 to − 0.28 Cm−2, were studied in NaCl and CaCl2 salt solutions at 1 M and 0.1 M concentrations to evaluate the effect of the surface charge, counterion valence, and concentration of added salt. We obtain that Na + and Ca2 + ions enter inside the soft nanoparticle. Monovalent ions are more accumulated inside the nanoparticle surface, whereas divalent ions are more accumulated just in the plane of the nanoparticle surface sites. The increasing of the the salt concentration has little effect on the internalization of counterions, but significantly reduces the number of water molecules that enter inside the nanoparticle. The manner of distributing the surface charge in the nanoparticle (uniformly over all surface sites or discretely over a limited set of randomly selected sites) considerably affects the distribution of counterions in the proximities of the nanoparticle surface.

Testing reciprocity in social interactions: A comparison between the Directional consistency and Skew symmetry statistics

In the present work we focus on two indices that quantify directionality and skew-symmetrical patterns in social interactions as measures of social reciprocity: the Directional consistency (DC) and Skew symmetry indices. Although both indices enable researchers to describe social groups, most studies require statistical inferential tests. The main aims of the present study are: firstly, to propose an overall statistical technique for testing null hypotheses regarding social reciprocity in behavioral studies, using the DC and Skew symmetry statistics (Φ) at group level; and secondly, to compare both statistics in order to allow researchers to choose the optimal measure depending on the conditions. In order to allow researchers to make statistical decisions, statistical significance for both statistics has been estimated by means of a Monte Carlo simulation. Furthermore, this study will enable researchers to choose the optimal observational conditions for carrying out their research, as the power of the statistical tests has been estimated.

The effect of skewness and kurtosis on the Kenward-Roger approximation when group distributions differ

This study examined the independent effect of skewness and kurtosis on the robustness of the linear mixed model (LMM), with the Kenward-Roger (KR) procedure, when group distributions are different, sample sizes are small, and sphericity cannot be assumed. Methods: A Monte Carlo simulation study considering a split-plot design involving three groups and four repeated measures was performed. Results: The results showed that when group distributions are different, the effect of skewness on KR robustness is greater than that of kurtosis for the corresponding values. Furthermore, the pairings of skewness and kurtosis with group size were found to be relevant variables when applying this procedure. Conclusions: With sample sizes of 45 and 60, KR is a suitable option for analyzing data when the distributions are: (a) mesokurtic and not highly or extremely skewed, and (b) symmetric with different degrees of kurtosis. With total sample sizes of 30, it is adequate when group sizes are equal and the distributions are: (a) mesokurtic and slightly or moderately skewed, and sphericity is assumed; and (b) symmetric with a moderate or high/extreme violation of kurtosis. Alternative analyses should be considered when the distributions are highly or extremely skewed and samples sizes are small.

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.

A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement -SCR-, under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

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.

Local noise analysis of a Schottky contact: combined thermionic-emissiondiffusion theory

A theoretical model for the noise properties of Schottky barrier diodes in the framework of the thermionic-emission¿diffusion theory is presented. The theory incorporates both the noise inducedby the diffusion of carriers through the semiconductor and the noise induced by the thermionicemission of carriers across the metal¿semiconductor interface. Closed analytical formulas arederived for the junction resistance, series resistance, and contributions to the net noise localized indifferent space regions of the diode, all valid in the whole range of applied biases. An additionalcontribution to the voltage-noise spectral density is identified, whose origin may be traced back tothe cross correlation between the voltage-noise sources associated with the junction resistance andthose for the series resistance. It is argued that an inclusion of the cross-correlation term as a newelement in the existing equivalent circuit models of Schottky diodes could explain the discrepanciesbetween these models and experimental measurements or Monte Carlo simulations.

Effect of long-range Coulomb interaction on shot-noise suppression in ballistic transport

We present a microscopic analysis of shot-noise suppression due to long-range Coulomb interaction in semiconductor devices under ballistic transport conditions. An ensemble Monte Carlo simulator self-consistently coupled with a Poisson solver is used for the calculations. A wide range of injection-rate densities leading to different degrees of suppression is investigated. A sharp tendency of noise suppression at increasing injection densities is found to scale with a dimensionless Debye length related to the importance of space-charge effects in the structure.

Universality of the 1/3 shot-noise suppression factor in nondegenerate diffusive conductors

Shot-noise suppression is investigated in nondegenerate diffusive conductors by means of an ensemble Monte Carlo simulator. The universal 1/3 suppression value is obtained when transport occurs under elastic collision regime provided the following conditions are satisfied: (i) The applied voltage is much larger than the thermal value; (ii) the length of the device is much greater than both the elastic mean free path and the Debye length. By fully suppressing carrier-number fluctuations, long-range Coulomb interaction is essential to obtain the 1/3 value in the low-frequency limit.