Asymptotic analysis of stock price densities and implied volatilities in mixed stochastic models

In this paper, we obtain sharp asymptotic formulas with error estimates for the Mellin con- volution of functions de ned on (0;1), and use these formulas to characterize the asymptotic behavior of marginal distribution densities of stock price processes in mixed stochastic models. Special examples of mixed models are jump-di usion models and stochastic volatility models with jumps. We apply our general results to the Heston model with double exponential jumps, and make a detailed analysis of the asymptotic behavior of the stock price density, the call option pricing function, and the implied volatility in this model. We also obtain similar results for the Heston model with jumps distributed according to the NIG law.

SQualTrack: A Tool for Robust Fault Detection

One of the techniques used to detect faults in dynamic systems is analytical redundancy. An important difficulty in applying this technique to real systems is dealing with the uncertainties associated with the system itself and with the measurements. In this paper, this uncertainty is taken into account by the use of intervals for the parameters of the model and for the measurements. The method that is proposed in this paper checks the consistency between the system's behavior, obtained from the measurements, and the model's behavior; if they are inconsistent, then there is a fault. The problem of detecting faults is stated as a quantified real constraint satisfaction problem, which can be solved using the modal interval analysis (MIA). MIA is used because it provides powerful tools to extend the calculations over real functions to intervals. To improve the results of the detection of the faults, the simultaneous use of several sliding time windows is proposed. The result of implementing this method is semiqualitative tracking (SQualTrack), a fault-detection tool that is robust in the sense that it does not generate false alarms, i.e., if there are false alarms, they indicate either that the interval model does not represent the system adequately or that the interval measurements do not represent the true values of the variables adequately. SQualTrack is currently being used to detect faults in real processes. Some of these applications using real data have been developed within the European project advanced decision support system for chemical/petrochemical manufacturing processes and are also described in this paper

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions. Methods: Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations. Results: We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001. Conclusion: Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia

Early Childhood Mathematics Education: Research, Curriculum and Educational Practice

This article reviews data obtained through research into early childhood mathematics education in Spain. It analyses the current curricular directions in mathematics education with early learners. It also provides an overview of mathematical practices in early childhood education classrooms to analyse the commonalities and differences between research, curriculum and educational practice. A review of the research presented at SEIEM symposia from 1997 until 2012 demonstrates: a) very little research has been done, a trend that is repeated in other areas, such as the JCR-Social Sciences Edition or the PME; b) the first steps have been taken to create a more and more cohesive body of research, although until now there has not been enough data to outline the curricular directions; and c) some discrepancies still exist between the mathematical practices in early childhood education classrooms and the official guidelines

Un análisis optimista de la educación matemática en la formación de maestros de educación infantil = An optimistic analysis of mathematics education in training pre-school teachers

This article offers a panorama of mathematics training for future teachers at pre-school level in Spain. With this goal in mind, this article is structured infour sections: where we come from, where we are, where we’re going and where we want to go. It offers, in short, a brief analysis that shows the efforts made to ensure there is sufficient academic and scientific rigour in teachers’ studies at pre-school in general and students’ mathematics education in particular. Together with a description of the progress made in recent years, it also raises some questions for all those involved in training future teachers for this educational stage

Cómo enseñar matemáticas en las primeras edades a partir de contextos de vida cotidiana = How to teach mathematics to young students based on everyday contexts

This paper stresses the importance of developing mathematical thought in young children based on everyday contexts, since these are meaningful learning situations with an interdisciplinary, globalised focus. The first part sets out the framework of reference that lays the theoretical foundations for these kinds of educational practices. The second part gives some teaching orientations for work based on everyday contexts. It concludes with the presentation of the activity 'We’re off to the cinema to learn mathematics!'

Matemáticas y juego = Mathematics and games

In this article we try to look at the learning of mathematics through games in the first years of schooling. The use of game resources in the class should not be carried out in a uniquely intuitive way but rather in a manner that contains some preliminary reflections such as, what do we understand by games? Why use games as a resource in the Mathematics classroom? And what does its use imply?

¿Para qué sirven los problemas en la clase de matemáticas? = What is the use of problems in Mathematics lessons?

The results obtained in several yield tests, at an international level (mainly the famous PISA 2003 report, by the OCDE), have raised a multiplicity of performances in order to improve the students' yield regarding problem solving. In this article we set a clear guideline on how problems should be used in Mathematics lessons, not for obtaining better scores in the yield tests but for improving the development of Mathematical thinking in students. From this perspective, the author analyses, through eight reflections, how the concept of problem, transmitted both in the school and from society, influences the students

Una visión actualizada de la didáctica de la matemática en educación infantil = An up-to-date vision of pre-school mathematics teaching

This article aims to investigate pre-school mathematics teaching from an uptodate perspective. To pursue this contemporary vision we focus on four key questions: what kind of maths is being worked on, who is doing it, how it is being done, and why it is being done