Catalina Bolancé

Kernel Density Estimation for Heavy-Tailed Distributions Using the Champernowne Transformation

When estimating loss distributions in insurance, large and small losses are usually split because it is difficult to find a simple parametric model that fits all claim sizes. This approach involves determining the threshold level between large and small losses. In this article, a unified approach to the estimation of loss distributions is presented. We propose an estimator obtained by transforming the data set with a modification of the Champernowne cdf and then estimating the density of the transformed data by use of the classical kernel density estimator. We investigate the asymptotic bias and variance of the proposed estimator. In a simulation study, the proposed method shows a good performance. We also present two applications dealing with claims costs in insurance.

Prediction of the economic cost of individual long-term care in the Spanish population

Pensions together with savings and investments during active life are key elements of retirement planning. Motivation for personal choices about the standard of living, bequest and the replacement ratio of pension with respect to last salary income must be considered. This research contributes to the financial planning by helping to quantify long-term care economic needs. We estimate life expectancy from retirement age onwards. The economic cost of care per unit of service is linked to the expected time of needed care and the intensity of required services. The expected individual cost of long-term care from an onset of dependence is estimated separately for men and women. Assumptions on the mortality of the dependent people compared to the general population are introduced. Parameters defining eligibility for various forms of coverage by the universal public social care of the welfare system are addressed. The impact of the intensity of social services on individual predictions is assessed, and a partial coverage by standard private insurance products is also explored. Data were collected by the Spanish Institute of Statistics in two surveys conducted on the general Spanish population in 1999 and in 2008. Official mortality records and life table trends were used to create realistic scenarios for longevity. We find empirical evidence that the public long-term care system in Spain effectively mitigates the risk of incurring huge lifetime costs. We also find that the most vulnerable categories are citizens with moderate disabilities that do not qualify to obtain public social care support. In the Spanish case, the trends between 1999 and 2008 need to be further explored.

Kernel density estimation of actuarial loss functions

Abstract In this paper we estimate actuarial loss functions based on a symmetrized version of the semiparametric transformation approach to kernel smoothing. We apply this method to an actuarial study of automobile claims. The method gives a good overall impression while estimating actuarial loss functions, since it is capable of estimating both the initial mode and the heavy tail that is so typical for actuarial and other economic loss distributions. We study the properties of the transformation kernel density estimation and show the differences with the multiplicative bias corrected estimator. We add insight into the kernel smoothing transformation method through an extensive simulation study with a particular view to the performance of the estimation at the tail.

Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions: An Approach Using R

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions estimated with parametric and non-parametric methods. The methods are implemented using the statistical package R. Parametric analysis is limited to estimation of normal and lognormal distributions for each of the two claim types. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described.

Loss risk through fraud in car insurance

Our objective is to analyse fraud as an operational risk for the insurance company. We study the effect of a fraud detection policy on the insurers results account, quantifying the loss risk from the perspective of claims auditing. From the point of view of operational risk, the study aims to analyse the effect of failing to detect fraudulent claims after investigation. We have chosen VAR as the risk measure with a non-parametric estimation of the loss risk involved in the detection or non-detection of fraudulent claims. The most relevant conclusion is that auditing claims reduces loss risk in the insurance company.

Allowance for the Age of Claims in Bonus-Malus Systems

The purpose of the paper is to use the age of claims in the prediction of risks. A dynamic random effects model on longitudinal count data is presented, and estimated on the portfolio of a major Spanish insurance company. The estimated autocorrelation coefficients of stationary random effects are decreasing. A consequence is that the predictive ability of a claim decreases with the lag between the period of risk prediction and the period of occurrence. There is a wide gap between the long term properties of actuarial and real-world experience rating schemes. This gap can be partly filled if the age of claims is taken into account in the actuarial model.

Intermediary and Structural Determinants of Early Childhood Health in Colombia: Exploring the Role of Communities

This study examines how structural determinants influence intermediary factors of child health inequities and how they operate through the communities where children live. In particular, we explore individual, family and community level characteristics associated with a composite indicator that quantitatively measures intermediary determinants of early childhood health in Colombia. We use data from the 2010 Colombian Demographic and Health Survey (DHS). Adopting the conceptual framework of the Commission on Social Determinants of Health (CSDH), three dimensions related to child health are represented in the index: behavioural factors, psychosocial factors and health system. In order to generate the weight of the variables and take into account the discrete nature of the data, principal component analysis (PCA) using polychoric correlations are employed in the index construction. Weighted multilevel models are used to examine community effects. The results show that the effect of household’s SES is attenuated when community characteristics are included, indicating the importance that the level of community development may have in mediating individual and family characteristics. The findings indicate that there is a significant variance in intermediary determinants of child health between-community, especially for those determinants linked to the health system, even after controlling for individual, family and community characteristics. These results likely reflect that whilst the community context can exert a greater influence on intermediary factors linked directly to health, in the case of psychosocial factors and the parent’s behaviours, the family context can be more important. This underlines the importance of distinguishing between community and family intervention programmes.

Time-varying credibility for frequency risk models: estimation and tests for autoregressive specifications on the random effects

Abstract This paper estimates and tests autoregressive specifications for dynamic random effects in a frequency risk model. Linear credibility predictors are derived from the estimators. Examples are provided from the automobile portfolio of a Spanish insurance company.

Social Determinants of Child Health in Colombia: Can Community Education Moderate the Effect of Family Characteristics?

Contextual effects on child health have been investigated extensively in previous research. However, few studies have considered the interplay between community characteristics and individual-level variables. This study examines the influence of community education and family socioeconomic characteristics on child health (as measured by height and weight-for-age Z-scores), as well as their interactions. We adapted the Commission on Social Determinants of Health (CSDH) framework to the context of child health. Using data from the 2010 Colombian Demographic and Health Survey (DHS), weighted multilevel models are fitted since the data are not self-weighting. The results show a positive impact of the level of education of other women in the community on child health, even after controlling for individual and family socioeconomic characteristics. Different pathways through which community education can substitute for the effect of family characteristics on child nutrition are found. The interaction terms highlight the importance of community education as a moderator of the impact of the mother’s own education and autonomy, on child health. In addition, the results reveal differences between height and weight-for-age indicators in their responsiveness to individual and contextual factors. Our findings suggest that community intervention programmes may have differential effects on child health. Therefore, their identification can contribute to a better targeting of child care policies.

Factors affecting hospital admission and recovery stay duration of in-patient motor victims in Spain.

Hospital expenses are a major cost driver of healthcare systems in Europe, with motor injuries being the leading mechanism of hospitalizations. This paper investigates the injury characteristics which explain the hospitalization of victims of traffic accidents that took place in Spain. Using a motor insurance database with 16,081 observations a generalized Tobit regression model is applied to analyse the factors that influence both the likelihood of being admitted to hospital after a motor collision and the length of hospital stay in the event of admission. The consistency of Tobit estimates relies on the normality of perturbation terms. Here a semi-parametric regression model was fitted to test the consistency of estimates, concluding that a normal distribution of errors cannot be rejected. Among other results, it was found that older men with fractures and injuries located in the head and lower torso are more likely to be hospitalized after the collision, and that they also have a longer expected length of hospital recovery stay.