The transition from a demographic regime of high mortality and high fertility to one with low mortality and low fertility is universal and comes along with the process of socio-economic modernization. The Spanish total fertility rate has decreased to below replacement levels in the last decades. The decline has persisted since the 1960s and is diverse across the country. Based on that diversity, the use of population forecasts, not only at national but at regional levels, for planning purposes (governments and private sector) with large horizons has become a must to provide essential services. Using a Bayesian hierarchical model we constructed probabilistic fertility forecasts for Spain at the regional level. Although this approach is already issued by the United Nations little research has been done focusing on the Spanish subnational level. Our objective is to disaggregate the national projections of the total fertility rate for Spain into regional forecasts. The results of this research will show the model fitting, first to the national level and then using a multifaceted and continuous evolution of fertility over time, at the regional level, to check its convergence.

Long-term ratings of companies are obtained from public data plus some additional nondisclosed information. A model based on data from firms’ public accounts is proposed to directly obtain these ratings, showing fairly close similitude with published results from Credit Rating Agencies. The rating models used to assess the creditworthiness of a firm may involve some possible conflicts of interest, as companies pay for most of the rating process and are, thus, clients of the rating firms. Such loss of faith among investors and criticism toward the rating agencies were especially severe during the financial crisis in 2008. To overcome this issue, several alternatives are addressed; in particular, the focus is on elaborating a rating model for Moody’s long-term companies’ ratings for industrial and retailing firms that could be useful as an external check of published rates. Statistical and artificial intelligence methods are used to obtain direct prediction of awarded rates in these sectors, without aggregating adjacent classes, which is usual in previous literature. This approach achieves an easy-to-replicate methodology for real rating forecasts based only on public available data, without incurring the costs associated with the rating process, while achieving a higher accuracy. With additional sampling information, these models can be extended to other sectors.

Las técnicas estocásticas y probabilísticas juegan un papel fundamental en la modelización matemática de aspectos relacionados con las ciencias naturales y sociales. En física, los modelos estocásticos son usados con frecuencia en áreas tan diversas como la climatología, la biología molecular, la bioquímica, así como en la economía. El propósito de este trabajo es el de plantear la aplicación a las finanzas de modelos y procesos utilizados en el campo de la física estadística, mediante técnicas y resultados de la teoría estocástica de procesos y en particular de procesos de difusión que, directamente surgidos y aplicados en el campo de la física tienen su utilidad en el campo de la economía financiera. En nuestro caso, se pretende relacionar la ecuación de Fokker-Planck con el modelo planteado por Black y Scholes dado que éste último es modelizado mediante una ecuación parcial diferencial estocástica y pueden establecerse similitudes con los procesos estocásticos y de difusión que se observan en la física.