Montserrat Guillén

Detection of Automobile Insurance Fraud With Discrete Choice Models and Misclassified Claims

The insurance industry is concerned with the detection of fraudulent behavior. The number of automobile claims involving some kind of suspicious circumstance is high and has become a subject of major interest for companies. This article demonstrates the performance of binary choice models for fraud detection and implements models for misclassification in the response variable. A database from the Spanish insurance market that contains honest and fraudulent claims is used. The estimation of the probability of omission provides an estimate of the percentage of fraudulent claims that are not detected by the logistic regression model.

Calculation of the Variance in Surveys of the Economic Climate

Public opinion surveys have become progressively incorporated into systems of official statistics. Surveys of the economic climate are usually qualitative because they collect opinions of businesspeople and/or experts about the long-term indicators described by a number of variables. In such cases the responses are expressed in ordinal numbers, that is, the respondents verbally report, for example, whether during a given trimester the sales or the new orders have increased, decreased or remained the same as in the previous trimester. These data allow to calculate the percent of respondents in the total population (results are extrapolated), who select every one of the three options. Data are often presented in the form of an index calculated as the difference between the percent of those who claim that a given variable has improved in value and of those who claim that it has deteriorated. As in any survey conducted on a sample the question of the measurement of the sample error of the results has to be addressed, since the error influences both the reliability of the results and the calculation of the sample size adequate for a desired confidence interval. The results presented here are based on data from the Survey of the Business Climate (Encuesta de Clima Empresarial) developed through the collaboration of the Statistical Institute of Catalonia (Institut d’Estadistica de Catalunya) with the Chambers of Commerce (Camaras de Comercio) of Sabadell and Terrassa.

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.

A Correlation Sensitivity Analysis of Non-Life Underwriting Risk in Solvency Capital Requirement Estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

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.

An Introduction to Parametric and Non-Parametric Models for Bivariate Positive Insurance Claim Severity Distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

Modelling different types of automobile insurance fraud behaviour in the Spanish market

Abstract From a microeconomic point of view, the control of insurance fraud requires a detailed knowledge of the insureds’ behaviour. In this paper, we present discrete-choice models for fraud behaviour and we estimate the influence of the insured and claim characteristics on the probability of committing fraud. Data correspond to a Spanish sample. Correction for choice-based sampling is introduced in the estimation due to the oversampling of fraud claims. The structure of the Spanish automobile insurance market is also discussed. Our results differ according to the type of fraud behaviour that is under consideration.

Risk classification for claim counts: A comparative analysis of various zero-inflated mixed Poisson and hurdle models

Abstract This paper presents and compares different risk classification models for the annual number of claims reported to the insurer. Generalized heterogeneous, zero-inflated, hurdle, and compound frequency models are applied to a sample of an automobile portfolio of a major company operating in Spain. A statistical comparison between models is performed with the help of various specification tests (Score and Hausman tests for nested models, Vuong test or information criteria for nonnested ones). Interesting results about claiming behavior are obtained.

Count data models for a credit scoring system

Credit scoring systems created for the evaluation of new applications are based on the available statistical information which is related to the behaviour of former clients with credit. Usually, financial institutions apply discriminant analysis techniques to create these systems but they lack of good properties due, for example, to the presence of non-normal variables. As an alternative, the future repayment behaviour is predicted by means of the expected number of unpaid instalments. The use of this latter variable suggests that appropriate models might be of interest, in which some covariant exogenous variables are included in order to specify the expected level of debt. At this point, prepayment is not explicitly considered. These models should be used as explanatory tools when evaluating the level of risk involved in personal credit transactions. Negative Binomial Distribution models are suitable when heterogeneity is taken into account. Some results related to prediction performance are shown for different model specifications in the case of data from a Spanish bank.