The mortality of the Italian population: Smoothing techniques on the Lee--Carter model

Several approaches have been developed for forecasting mortality using the stochastic model. In particular, the Lee-Carter model has become widely used and there have been various extensions and modifications proposed to attain a broader interpretation and to capture the main features of the dynamics of the mortality intensity. Hyndman-Ullah show a particular version of the Lee-Carter methodology, the so-called Functional Demographic Model, which is one of the most accurate approaches as regards some mortality data, particularly for longer forecast horizons where the benefit of a damped trend forecast is greater. The paper objective is properly to single out the most suitable model between the basic Lee-Carter and the Functional Demographic Model to the Italian mortality data. A comparative assessment is made and the empirical results are presented using a range of graphical analyses.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS394 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Profit participation annuities: a business profitability analysis within a demographic risk sensitive approach

The aim of the paper is to analyze the performance of a portfolio of participating life annuities, focusing on the minimum acceptable income level throughout the quantiles of the return distribution. The model, in addition to the necessary consideration of the volatility of financial markets, gives a central role to the impact of the longevity phenomenon. The sensitivity of the portfolio performance to the survival projection, the presence of a break-even point and the time of optimum performance are pointed out, under different hypotheses for the participating quota and with stochastic assumption for the accumulation and the discounting financial processes and for the survival description

Extending the Lee Carter Model: a Three-way Decomposition

In this paper, we focus on a Multidimensional Data Analysis approach to the Lee-Carter (LC) model of mortality trends . In particular, we extend the bilinear LC model and specify a new model based on a three-way structure, which incorporates a further component in the decomposition of the log-mortality rates. A multi-way component analysis is performed using the Tucker 3 model. The suggested methodology allows us to obtain combined estimates for the three modes: i) time, ii) agegroups and iii) different populations. From the results obtained by the Tucker 3 decomposition, we can jointly compare, in both a numerical and graphical way, the relationships among all three modes and obtain a time series component as a leading indicator of the mortality trend for a group of populations. Further, we carry out a correlation analysis of the estimated trends in order to assess the reliability of the results of the three-way decomposition. The model’s goodness of fit is assessed using an analysis of the residuals. Finally, we discuss how the synthesised mortality index can be used to build concise projected life tables for a group of populations. An application which compares ten European countries is used to illustrate the approach and provide a deeper insight into the model and its implementation

Multiple mortality modeling in Poisson Lee-Carter framework

The academic literature in longevity field has recently focused on models for detecting multiple population trends (D'Amato et al., 2012b; Njenga and Sherris, 2011; Russolillo et al., 2011, etc.). In particular, increasing interest has been shown about "related" population dynamics or "parent" populations characterized by similar socioeconomic conditions and eventually also by geographical proximity. These studies suggest dependence across multiple populations and common long-run relationships between countries (for instance, see Lazar et al., 2009). In order to investigate cross-country longevity common trends, we adopt a multiple population approach. The algorithm we propose retains the parametric structure of the Lee-Carter model, extending the basic framework to include some cross-dependence in the error term. As far as time dependence is concerned, we allow for all idiosyncratic components (both in the common stochastic trend and in the error term) to follow a linear process, thus considering a highly flexible specification for the serial dependence structure of our data. We also relax the assumption of normality, which is typical of early studies on mortality (Lee and Carter, 1992) and on factor models (see e.g., the textbook by Anderson, 1984). The empirical results show that the multiple Lee-Carter approach works well in the presence of dependence

Computational framework for longevity risk management

Longevity risk threatens the financial stability of private and government sponsored defined benefit pension systems as well as social security schemes, in an environment already characterized by persistent low interest rates and heightened financial uncertainty. The mortality experience of countries in the industrialized world would suggest a substantial age-time interaction, with the two dominant trends affecting different age groups at different times. From a statistical point of view, this indicates a dependence structure. It is observed that mortality improvements are similar for individuals of contiguous ages (Wills and Sherris, Integrating financial and demographic longevity risk models: an Australian model for financial applications, Discussion Paper PI-0817, 2008). Moreover, considering the dataset by single ages, the correlations between the residuals for adjacent age groups tend to be high (as noted in Denton et al., J Population Econ 18:203-227, 2005). This suggests that there is value in exploring the dependence structure, also across time, in other words the inter-period correlation. In this research, we focus on the projections of mortality rates, contravening the most commonly encountered dependence property which is the "lack of dependence" (Denuit et al., Actuarial theory for dependent risks: measures. Orders and models, Wiley, New York, 2005). By taking into account the presence of dependence across age and time which leads to systematic over-estimation or under-estimation of uncertainty in the estimates (Liu and Braun, J Probability Stat, 813583:15, 2010), the paper analyzes a tailor-made bootstrap methodology for capturing the spatial dependence in deriving confidence intervals for mortality projection rates. We propose a method which leads to a prudent measure of longevity risk, avoiding the structural incompleteness of the ordinary simulation bootstrap methodology which involves the assumption of independence

Establishment of the size of portions of fruit and vegetable consumption for use in food guides in the Spanish environment: proposal of the Scientific Committee of the 5 a day Association

[EN] Introduction: Food servings are standard amounts of food stuffs or drinks to help dietetic advice to promote and preserve health. The aim is to establish the serving size of fruits and vegetables (FH) to be used in food based dietary guidelines (FBDG). Material and Methods: Methodology of the United States Department of Agriculture (USDA) was adapted to establish serving sizes for FBDG, along of the followed by the food exchange system. Data was collected from the FH portion sizes reported in nutritional surveys and common sizes available in the Spanish market, and they were adjusted to an easily recognisable quantities of food with equivalence on key nutrients: the compliance with public health goals for FH consumption was evaluated. Results: Portion sizes typically reported in Spanish nutrition surveys are scarce and not homogeneous, and no data published in scientific journals on portion sizes were available. The Spanish FBDG, in spite of showing a range of serving size for FH, do not assure that they are interchangeable nor specify the method to obtein them.The serving of vegetables was 139,44g (DS:+/- 21.98, CV:0.16), 137,68g (DS:+/- 49,61, CV:0,36) for fruits and 28.00g (DS:+/- 7,53, CV:0.27) for dried fruits. Conclusions: With the established servings, the recommendation of consuming "at least 5 servings of FH a day" would allow reaching the Public Health goals for FH established in 600g (net weight)/person/day. It is recommended that the Spanish Agency for Consumers, Food Safety and Nutrition (AECOSAN) uses this methodology to establish serving sizes for the rest of food groups that make up the FBDG for the Spanish population.[ES] Introducción: Las raciones de consumo son cantidades estándar de alimentos o bebidas sugeridas para asesorar sobre la cantidad de alimento a consumir para preservar un estado de salud adecuado. El objetivo principal de este trabajo es establecer los tamaños de ración de consumo de frutas y hortalizas (FH) para uso en guías alimentarias. Material y Métodos: Se adaptó la metodología de la United States Department of Agriculture (USDA) para el establecimiento de los tamaños de ración de consumo para guías, y la del Sistema de Intercambios. Se recopilaron datos de porción reportados en encuestas y calibres comunes en el mercado, se ajustó a cantidades de alimento fácilmente reconocibles y con equivalencia de nutrientes clave y se evaluó el grado de cumplimiento de los objetivos de salud pública para el consumo de FH. Resultados: Los tamaños de porción típicamente reportados en encuestas españolas son escasos y poco homogéneos, y no se encontraron datos publicados en revistas científicas sobre los calibres. Las guías alimentarias españolas, a pesar de mostrar un rango de tamaño de ración para FH no aseguran que sean intercambiables ni especifican el método para llegar a las mismas. La ración de hortalizas obtenida ha sido de 139,44g (DS:±21,98; CV:0,16), de 137,68g (DS:±49,61; CV:0,36) para frutas y 28,00g (DS:±7,53; CV:0,27) para frutas desecadas. . Conclusiones: Con las raciones establecidas, el mensaje ¿consume al menos 5 raciones entre FH al día¿ permitiría alcanzar los objetivo de Salud Pública para FH establecidos en 600g (peso neto)/persona/día. Se recomienda a la Agencia Española de Consumo, Seguridad Alimentaria y Nutrición (AECOSAN) que use esta misma metodología para el establecimiento de raciones en el resto de grupos de alimentos que configuran la Guía Dietética Basada en Alimentos para la población española.Russolillo, G.; Baladia, E.; Moñino, M.; Marques-Lopes, I.; Farran, A.; Bonany, J.; Gilabert, V.... (2019). Establecimiento del tamaño de raciones de consumo de frutas y hortalizas para su uso en guías alimentarias en el entorno español: propuesta del Comité Científico de la Asociación 5 al día. Revista Española de Nutrición Humana y Dietética (Online). 23(4):205-221. https://doi.org/10.14306/renhyd.23.4.628S20522123

Recomendaciones de manipulación doméstica de frutas y hortalizas para preservar su valor nutritivo

The health benefits of daily consumption of at least 5 portions of a variety of fruit and vegetables are well documented. The World Health Organization (WHO) public health goal, established in 600 grams per person/day, is not achieved in Spain, so it is important to improve access to these foods, maintain their potential nutritive value and overcome barriers for their consumption. The objectives of this paper are: facilitate responsible decision-making regarding health; maximize the nutritional value of fruit and vegetables, help overcome barriers for fruit and vegetables consumption and report on how their storage at home, their handling and cooking affect to nutritional value of fruit and vegetables.In order to minimize nutrients loss and improve their bioavailability during fruit and vegetables handling, the Association for the promotion of fruit and vegetables “5 a day” (Spain) recommends: avoid prolonged storage of fruit and vegetables in the fridge; use layers and outer leaves; peel and/or cut them just before consumption; wash the whole pieces and then chop them; controlling the soaking time of cut pieces; prefer cooking techniques that do not require direct contact with water; a shorter cooking time, less loss of nutrients; the correct frying retains nutrients very well, although it is a technique of which should not be abused; add a few drops of vinegar or lemon juice to the cooking water if it does not change the taste and dish acceptance; use the water of cooking to elaborate other foods (e.g. sauces, soups, purees, etc.) except those coming from chard, spinach or beets. The “5 a day” Association (Spain) recommends increasing consumption of fruit and vegetables, and state that theloss of nutrients during their home handling should not be understood as a barrier for their consumption.El beneficio para la salud del consumo diario de al menos 5 raciones entre frutas y hortalizas está bien documentado. En España no se alcanzan los 600 gramos por persona y día que recomienda la Organización Mundial de la Salud (OMS) en sus objetivos de salud pública, por lo que es importante mejorar el acceso a estos alimentos, aprovechar su potencial nutritivo y salvar las barreras para su consumo. Los objetivos de este documento son: facilitar la toma de decisiones responsables con la salud; aprovechar al máximo el valor nutritivo de frutas y hortalizas; ayudar a salvar las barreras para su consumo e informar sobre cómo afecta la conservación, manipulación y cocinado domésticos a su valor nutritivo.Para minimizar la pérdida de nutrientes y mejorar su biodisponibilidad durante la manipulación de frutas y hortalizas, la Asociación para la promoción del consumo de frutas y hortalizas “5 al día” (España) recomienda: evitar almacenamientos prolongados en el refrigerador; aprovechar las capas y hojas exteriores; pelar y/o cortar el alimento justo antes de consumirlo; lavar las piezas enteras y trocearlas posteriormente; controlar el tiempo de remojo de las piezas cortadas; preferir técnicas de cocinado que no requieran contacto directo con el agua; a menor tiempo de cocción, menor pérdida de nutrientes; la fritura correcta conserva muy bien los nutrientes, aunque no debe abusarse de esta técnica; añadir un chorrito de vinagre o de zumo de limón al agua de cocción; aprovechar el agua de los vegetales cocidos para elaborar otros alimentos (ej.: salsas, sopas, purés, etc.), excepto la de acelgas, espinacas o remolacha. La Asociación “5 al día” recomienda aumentar el consumo de frutas y hortalizas, y considera que la pérdida de nutrientes durante su manipulación doméstica no debe entenderse como una barrera para su consumo

Recomendaciones de manipulación doméstica de frutas y hortalizas para preservar su valor nutritivo

El beneficio para la salud del consumo diario de al menos 5 raciones entre frutas y hortalizas está bien documentado. En España no se alcanzan los 600 gramos por persona y día que recomienda la Organización Mundial de la Salud (OMS) en sus objetivos de salud pública, por lo que es importante mejorar el acceso a estos alimentos, aprovechar su potencial nutritivo y salvar las barreras para su consumo. Los objetivos de este documento son: facilitar la toma de decisiones responsables con la salud; aprovechar al máximo el valor nutritivo de frutas y hortalizas; ayudar a salvar las barreras para su consumo e informar sobre cómo afecta la conservación, manipulación y cocinado domésticos a su valor nutritivo. Para minimizar la pérdida de nutrientes y mejorar su biodisponibilidad durante la manipulación de frutas y hortalizas, la Asociación para la promoción del consumo de frutas y hortalizas"5 al día" (España) recomienda: evitar almacenamientos prolongados en el refrigerador; aprovechar las capas y hojas exteriores; pelar y/o cortar el alimento justo antes de consumirlo; lavar las piezas enteras y trocearlas posteriormente; controlar el tiempo de remojo de las piezas cortadas; preferir técnicas de cocinado que no requieran contacto directo con el agua; a menor tiempo de cocción, menor pérdida de nutrientes; la fritura correcta conserva muy bien los nutrientes, aunque no debe abusarse de esta técnica; añadir un chorrito de vinagre o de zumo de limón al agua de cocción; aprovechar el agua de los vegetales cocidos para elaborar otros alimentos (ej.: salsas, sopas, purés, etc.), excepto la de acelgas, espinacas o remolacha. La Asociación"5 al día" recomienda aumentar el consumo de frutas y hortalizas, y considera que la pérdida de nutrientes durante su manipulación doméstica no debe entenderse como una barrera para su consumo