A Comparison of Forecasting Mortality Models Using Resampling Methods

[EN] The accuracy of the predictions of age-specific probabilities of death is an essential objective for the insurance industry since it dramatically affects the proper valuation of their products. Currently, it is crucial to be able to accurately calculate the age-specific probabilities of death over time since insurance companies' profits and the social security of citizens depend on human survival; therefore, forecasting dynamic life tables could have significant economic and social implications. Quantitative tools such as resampling methods are required to assess the current and future states of mortality behavior. The insurance companies that manage these life tables are attempting to establish models for evaluating the risk of insurance products to develop a proactive approach instead of using traditional reactive schemes. The main objective of this paper is to compare three mortality models to predict dynamic life tables. By using the real data of European countries from the Human Mortality Database, this study has identified the best model in terms of the prediction ability for each sex and each European country. A comparison that uses cobweb graphs leads us to the conclusion that the best model is, in general, the Lee-Carter model. Additionally, we propose a procedure that can be applied to a life table database that allows us to choose the most appropriate model for any geographical area.The research of David Atance was supported by a grant (Contrato Predoctoral de Formacion Universitario) from the University of Alcala. This work is partially supported by a grant from the MEIyC (Ministerio de Economia, Industria y Competitividad, Spain project ECO2017-89715-P).Atance, D.; Debón Aucejo, AM.; Navarro, E. (2020). A Comparison of Forecasting Mortality Models Using Resampling Methods. Mathematics. 8(9):1-21. https://doi.org/10.3390/math8091550S12189BOOTH, H., MAINDONALD, J., & SMITH, L. (2002). 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Un nuevo modelo dinámico de mortalidad basado en la edad clave y uso de técnicas de remuestreo para su evaluación

El objetivo de esta tesis está relacionado con tratar de minimizar el riesgo de longevidad mediante su adecuada modelización. Así, se va a desarrollar un modelo dinámico de mortalidad que está centrado en estudiar los cambios y/o variaciones que sufren las tasas de mortalidad de un año a otro. El modelo que aquí se presenta, asume que las variaciones que se producen en la curva de mortalidad están linealmente relacionadas con un número reducido de factores. Estos factores de riesgo se corresponden con una o varias tasas de mortalidad de una edad concreta, es decir, dicho factor o factores de riesgo se identifican con las variaciones de las tasas de mortalidad de lo que denominaremos “edades clave”. Una de las principales ventajas del modelo es que la tasa de mortalidad de la edad clave es totalmente observable y contrasta con el resto de los modelos alternativos que capturan la dinámica de la mortalidad a través de un parámetro que no es observable. Tras una primera propuesta de un nuevo modelo de mortalidad basado en la edad clave, se proponen varias mejoras a ese modelo, utilizar máxima verosimilitud en la estimación de los parámetros, estimar todos los parámetros en un único paso y reducir de manera significativa el número de parámetros a solo seis. También a modo de ejemplo, se ha calculado el V@R y CV@R, dos medidas desarrolladas para gestionar el riesgo de longevidad y que ponen de manifiesto la capacidad del modelo de cara a su utilización para la medición a largo plazo del riesgo de longevidad. Por último, se describe la utilidad y simplicidad de utilizar los métodos de remuestreo como herramienta para medir la capacidad predictiva de los modelos de mortalidad. Conviene señalar que representa una novedad la utilización de estos métodos para calibrar la capacidad predictiva de datos en forma de panel y en especial, para datos de mortalidad. Además, los resultados se van a mostrar mediante la utilización de los gráficos de radar, una herramienta muy interesante para resumir y ordenar la capacidad predictiva de diferentes modelos

Valuation of reverse mortgages in the Spanish market for foreign residents

The continuous growth in life expectancy, besides to the difficult economic and financial situation of the public pension system in Spain, makes reverse mortgages an attractive solution for providing additional income to retirees. However, despite being almost 20 years old, the Spanish market remains immature. Consequently, providers face significant risks, due to factors such as interest rates, housing prices, and longevity. Numerous tourists visit Spain, and many retire there, obtaining legal residence. Therefore, lenders could be interested in marketing reverse mortgages to foreign residents. Nevertheless, the longevity risk faced by these lenders may differ depending on the nationality of the borrower, and profits and losses could vary. Consequently, we propose a methodology for comparing the pricing of reverse mortgages in Spain by considering differences in longevity risk. Specifically, we calculate the amount offered by three types of reverse mortgages to customers of different nationalities, genders, and ages with contracts made in Spain. Our conclusions are pertinent to Spanish lenders since the results indicate that, in general, a Spanish lender would assume a slightly larger risk when lending reverse mortgages to borrowers of the selected nationalities, regardless of other considerations, such as legal issues, which are not addressed in this article. First published online 31 October 202

Convergence and divergence in mortality: A global study from 1990 to 2030

An empirical question that has motivated demographers is whether there is convergence or divergence in mortality/longevity around the world. The epidemiological transition is the starting point for studying a global process of mortality convergence. This manuscript aims to provide an update on the concept of mortality convergence/divergence. We perform a comprehensive examination of nine different mortality indicators from a global perspective using clustering methods in the period 1990-2030. In addition, we include analyses of projections to provide insights into prospective trajectories of convergence clubs, a dimension unexplored in previous work. The results indicate that mortality convergence clubs of 194 countries by sex resemble the configuration of continents. These five clubs show a common steady upward trend in longevity indicators, accompanied by a progressive reduction in disparities between sexes and between groups of countries. Furthermore, this paper shows insights into the historical evolution of the convergence clubs in the period 1990-2020 and expands their scope to include projections of their expected future evolution in 2030

A meta-analysis and critical review of prospective memory in autism spectrum disorder

Prospective memory (PM) is the ability to remember to carry out a planned intention at an appropriate moment in the future. Research on PM in ASD has produced mixed results. We aimed to establish the extent to which two types of PM (event-based/time-based) are impaired in ASD. In part 1, a meta-analysis of all existing studies indicates a large impairment of time-based, but only a small impairment of event-based, PM in ASD. In Part 2, a critical review concludes that time-based PM appears diminished in ASD, in line with the meta-analysis, but that caution should be taken when interpreting event-based PM findings, given potential methodological limitations of several studies. Clinical implications and directions for future research are discussed

Pathogen reduction/inactivation of products for the treatment of bleeding disorders:what are the processes and what should we say to patients?

Patients with blood disorders (including leukaemia, platelet function disorders and coagulation factor deficiencies) or acute bleeding receive blood-derived products, such as red blood cells, platelet concentrates and plasma-derived products. Although the risk of pathogen contamination of blood products has fallen considerably over the past three decades, contamination is still a topic of concern. In order to counsel patients and obtain informed consent before transfusion, physicians are required to keep up to date with current knowledge on residual risk of pathogen transmission and methods of pathogen removal/inactivation. Here, we describe pathogens relevant to transfusion of blood products and discuss contemporary pathogen removal/inactivation procedures, as well as the potential risks associated with these products: the risk of contamination by infectious agents varies according to blood product/region, and there is a fine line between adequate inactivation and functional impairment of the product. The cost implications of implementing pathogen inactivation technology are also considered

A simplified model for measuring longevity risk for life insurance products

Abstract In this paper, we propose a simple dynamic mortality model to fit and forecast mortality rates for measuring longevity and mortality risks. This proposal is based on a methodology for modelling interest rates, which assumes that changes in spot interest rates depend linearly on a small number of factors. These factors are identified as interest rates with a given maturity. Similarly, we assume that changes in mortality rates depend linearly on changes in a specific mortality rate, which we call the key mortality rate. One of the main advantages of this model is that it allows the development of an easy to implement methodology to measure longevity and mortality risks using simulation techniques. Particularly, we employ the model to calculate the Value-at-Risk and Conditional-Value-at-Risk of an insurance product testing the accuracy and robustness of our proposal using out-of-sample data from six different populations

Constructing dynamic life tables with a single factor model

45 p.En este trabajo se desarrollará un modelo unifactorial para explicar la dinámica de las tasas de mortalidad y abordar el riesgo relacionado con ésta. El factor seleccionado para explicar el comportamiento de la curva de mortalidad será la tasa de mortalidad correspondiente a una edad clave, y, mediante un análisis empírico de las poblaciones masculina y femenina de Francia y España, se pondrá de manifiesto que este enfoque produce resultados, al menos tan buenos, como los logrados por otros modelos bastante más complejos. Este planteamiento, basado en la edad clave, presenta varias ventajas frente a otras alternativas de la literatura. En efecto, el factor de riesgo (la edad clave) es totalmente observable, y la metodología puede extenderse fácilmente mediante la incorporación de factores adicionales (más edades clave), el estudio del efecto cohorte, el análisis de causas específicas de mortalidad o la consideración de sólo algunos tramos específicos dentro de la curva de mortalidad. Por otro lado, debe señalarse que este modelo, basado en edades clave, se ha inspirado en estudios previos sobre la dinámica de la curva de tipos de interés, por lo que gran parte de las metodologías desarrolladas para tipos de interés serían fácilmente adaptables al estudio de problemas relacionados con el riesgo de longevidad.The paper deals with the mortality risk evolution and presents a one factor model explaining the dynamics of all of the mortality rates. The selected factor will be the mortality rate at the key age, and an empirical study involving males and females in France and Spain will reveal that the present approach is not outperformed by more complex factor models. The key age seems to reflect several advantages with respect to other factors available in the literature. Actually, it is totally observable, and the methodology may be easily extended so as to incorporate more factors (more key ages), a cohort effect, specific mortality causes or specific ages. Furthermore, the choice of a key age as an explanatory factor is inspired by former studies about the interest rates dynamics, which allows us to draw on the model in order to address some longevity risk linked problems. Indeed, one only has to slightly modify some interest rate linked methodologies

Variabilidad genética de las razas ovinas de la Comunidad de Madrid, churra, rubia del Molar y colmenareña

Resumen de la comunicación presentada al III Congreso Ibérico sobre Recursos Genéticos Animales