El modelo de regresión de Cox

Darrera actualització: maig de 2022Este material docente forma parte de la asignatura de Análisis de Supervivencia y recoge las principales características de modelo de regresión de Cox de riesgos proporcionales

Cálculo de reservas con modelos lineales generalizados mixtos haciendo uso del software R

[eng] It is presented an application of generalized linear mixed models to the claim reserving problem, when data is of individual type, that generally corresponds to RBNS (Reported But Not Settled) claims. Reserves by years of origin and total are calculated and, with parametric bootstrap, predictive distributions of these reserves are estimated. Generalized linear mixed models are estimated using frequentist statistic. The used software is R, especially the lme4 package, although it is also used SAS. Results are compared with those of the Chain-Ladder method.[cat] Se presenta una aplicación de los modelos lineales generalizados mixtos al cálculo de provisiones cuando los datos son de tipo individual que, en general, se corresponden con datos de siniestros RBNS (Reported But Not Settled). Se calculan las reservas por años de ocurrencia y total y, con bootstrap paramétrico, se estiman las distribuciones predictivas de dichas reservas. Los modelos lineales generalizados mixtos se estiman utilizando estadística frecuentista. El software utilizado es R, en especial el paquete lme4, aunque también se utiliza SAS. Se comparan los resultados con los del método Chain-Ladde

The date predicted 200.000 cases of Covid-19 in Spain

The aim of this study is predicted 200.000 cases of Covid-19 in Spain. Covid-19 Spanish confirmed data obtained from Worldometer from 01 March 2020 - 17 April 2020. The data from 01 March 2020 - 10 April 2020 using to fitting with data from 11 April - 17 April 2020. For the evaluation of the forecasting accuracy measures, we use mean absolute percentage error (MAPE). Based on the results of SutteARIMA fitting data, the accuracy of SutteARIMA for the period 11 April 2020 - 17 April 2020 is 0.61% and we forecast 20.000 confirmed cases of Spain by the WHO situation report day 90/91 which is 19 April 2020 / 20 April 2020

Provisions for claims outstanding, incurred but not reported, with generalized linear models: prediction error formulated according to calendar year

In the current context of Solvency II, insurance companies are required to implement demanding business risk management systems. An important aspect of this risk management is the problem of technical provisions in non-life insurance and, as such, it is in the interest of insurers to calculate the prediction error that has occurred when using methodology to estimate a company's future payments. Furthermore, the predictive distribution of the fitted values, which is descriptive of the risk, allows us to estimate, for example, its Value at Risk at a given confidence level. In this paper we focus on the application of generalized linear models to the amounts of claim losses of a run-off triangle. In order to achieve error distribution, a parameter dependent parametric family is assumed, along with the logarithmic link function. The parametric family has as particular cases the Poisson, the Gamma and the Inverse Gaussian distributions. The particular case which assumes an (over-dispersed) Poisson distribution with the logarithmic link is widely known because it offers the same provision estimation as the deterministic Chain-Ladder method. In this study we develop formulas of the prediction error of future payments by calendar years for the general parametric family. This allows us to perform calculations that consider a financial environment, whether employing analytical formulation or bootstrap estimation. In practice, the presented formulations allow a determination to be made of the present value of the incurred but not reported claim of future payments including a risk margin with statistical significance

Bootstrapping pairs in Distance-Based Regression

Distance-based regression is a prediction method consisting of two steps: from distances between observations we obtain latent variables which, in turn, are the regressors in an ordinary least squares linear model. Distances are computed from actually observed predictors by means of a suitable dissimilarity function. Being in general nonlinearly related with the response their selection by the usual F tests is unavailable. In this paper we propose a solution to this predictor selection problem, by defining generalized test statistics and adapting a non-parametric bootstrap method to estimate their p-values. We include a numerical example with automobile insurance data.non-parametric bootstrap, automobile insurance data, predictors selection, distance-based regression

On which socioeconomic groups do reverse mortgages have the greatest impact? Evidence from Spain

Reverse mortgage is one of the products (perhaps the main one) that is good to obtain additional income by using the habitual residence as collateral. The main objective of this paper is to analyse the effects that reverse mortgage contracting has on household finances over the lifetime of a family according to the socioeconomic group to which it belongs in Spain. Four indicators are employed to measure the immediate and long-term effects. We use a stochastic model with a double source of randomness, survival and entry into dependency, and apply it to the three socioeconomic groups obtained with cluster methodology from the 2017 Spanish Household Financial Survey data. We conclude that the effects are very different dependingon the group: regarding only the effects of hiring a reverse mortgage on the income of the family, widowed women aged between 81 and 85 years, with low income and expenses as well as little net wealth, and a habitual residence that represents half of her net wealth (Cluster 1) are the most benefited; considering that the highest impact indicators are on the probability of illiquidity and on the value of lack of liquidity, the use of reverse mortgages benefits more the families in Cluster 3 (high income and expenses and really high net wealth, head of household aged between 76 and 80 years) and less the families in Cluster 2 (medium income, net wealth and expenses, head of household aged between 65 and 75 years)

Role of Private Long-Term Care Insurance in Financial Sustainability for an Aging Society

This work analyzes and quantifies the significance of private long-term care insurance for the elderly in protecting families from the increased expenses derived from dependency. We propose an economic and financial model for consumption and income deficit evolution. Survival/dependency are modeled by a Markov process with stochastic simulation techniques to obtain random variable distributions. Based on the Spanish survey of household finances data, Spanish families are classified using a cluster analysis for the wealth decumulation period. The conclusion is that, for a generic family, hiring long-term care insurance causes a significant reduction in the probability of lack of liquidity, the mean first time of lack of liquidity (if it occurs), and the mean present value of overall liquidity needs. It is also observed that there are important di erences between these impacts on different groups of families. These results show that hiring long-term care insurance would considerably lower financial problems in the decumulation period

Reverse mortgage and financial sustainability

This paper analyzes the effects that contracting a reverse mortgage has on the finances of families of a country or group whose members who aged 65 or older are the sole owners of the 100% of the property, regardless of the receipt of a retirement pension. For this purpose, an economic-financial model based on the life cycle model is defined, which considers a double source of randomness: mortality and dependence of family members. Long-term effects are measured using probabilistic, temporal and monetary indicators. For each country, the model must be adapted according to the legal framework for retirement and long-term care benefits and for the actuarial mortality and long-term care tables. As an illustration, this model was applied on Spanish families using data from the Spanish Survey of Household Finances 2017. The results obtained indicate that a family in Spain that meets the conditions for contracting a reverse mortgage sees, on average, an increase in its initial income and a decrease in both its probability of having liquidity problems in the future and the value of this lack of liquidity. It is also concluded that family composition influences the magnitude of these positive effects

Provisiones técnicas por años de calendario mediante modelo lineal generalizado: una aplicación con Rexcel

El Modelo Lineal Generalizado (MLG) es un modelo estocástico con aplicación al cálculo de provisiones técnicas. El MLG tiene como caso particular el método determinista Chain-Ladder (CL), y permite calcular los errores cometidos en la predicción. Dichos errores posibilitan el cálculo de márgenes de solvencia con sentido estadístico, objetivo primordial en Solvencia II. En este artículo se estudi an las fórmulas de las reservas por años de calendario, las cuales permiten cálculos en un entorno financiero. Acompañando el estudio se incluye una aplicación de RExcel que calcula valores actuales para diferentes escenarios, con fórmulas analíticas o distribuciones predictivas