Miguel Santolino

Beyond Value‐at‐Risk: GlueVaR Distortion Risk Measures

We propose a new family of risk measures, called GlueVaR, within the class of distortion risk measures. Analytical closed-form expressions are shown for the most frequently used distribution functions in financial and insurance applications. The relationship between GlueVaR, value-at-risk, and tail value-at-risk is explained. Tail subadditivity is investigated and it is shown that some GlueVaR risk measures satisfy this property. An interpretation in terms of risk attitudes is provided and a discussion is given on the applicability in nonfinancial problems such as health, safety, environmental, or catastrophic risk management.

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.

Indicators for the characterization of discrete Choquet integrals

Ordered weighted averaging (OWA) operators and their extensions are powerful tools used in numerous decision-making problems. This class of operator belongs to a more general family of aggregation operators, where each operator of this family is understood as a discrete Choquet integral. Aggregation operators are usually characterized by indicators. In this article four indicators usually associated with the OWA operator are extended to the discrete Choquet integral: namely, the degree of balance, the divergence, the variance indicator and Renyi entropies. All of these indicators are considered from a local and a global perspective. Linearity of indicators for linear combinations of capacities is investigated and, to illustrate the usefulness of results, indicators of the probabilistic ordered weighted averaging (POWA) operator are derived. Finally, a numerical example is provided to discuss the results in a specific context.

The use of flexible quantile-based measures in risk assessment

ABSTRACT A new family of distortion risk measures—GlueVaR—is proposed in Belles-Sampera et al. (2014) to procure a risk assessment lying between those provided by common quantile-based risk measures. GlueVaR measures may be expressed as a combination of these standard risk measures. We show here that this relationship may be used to obtain approximations of GlueVaR measures for general skewed distribution functions using the Cornish–Fisher expansion. A subfamily of GlueVaR measures satisfies the tail-subadditivity property. An example of risk measurement based on real insurance claim data is presented, where implications of tail-subadditivity in the aggregation of risks are illustrated.

Prevalence of alcohol-impaired drivers based on random breath tests in a roadside survey in Catalonia (Spain).

Sobriety checkpoints are not usually randomly located by traffic authorities. As such, information provided by non-random alcohol tests cannot be used to infer the characteristics of the general driving population. In this paper a case study is presented in which the prevalence of alcohol-impaired driving is estimated for the general population of drivers. A stratified probabilistic sample was designed to represent vehicles circulating in non-urban areas of Catalonia (Spain), a region characterized by its complex transportation network and dense traffic around the metropolis of Barcelona. Random breath alcohol concentration tests were performed during spring 2012 on 7596 drivers. The estimated prevalence of alcohol-impaired drivers was 1.29%, which is roughly a third of the rate obtained in non-random tests. Higher rates were found on weekends (1.90% on Saturdays and 4.29% on Sundays) and especially at night. The rate is higher for men (1.45%) than for women (0.64%) and it shows an increasing pattern with age. In vehicles with two occupants, the proportion of alcohol-impaired drivers is estimated at 2.62%, but when the driver was alone the rate drops to 0.84%, which might reflect the socialization of drinking habits. The results are compared with outcomes in previous surveys, showing a decreasing trend in the prevalence of alcohol-impaired drivers over time.

Copula-based regression modeling of bivariate severity of temporary disability and permanent motor injuries.

The analysis of factors influencing the severity of the personal injuries suffered by victims of motor accidents is an issue of major interest. Yet, most of the extant literature has tended to address this question by focusing on either the severity of temporary disability or the severity of permanent injury. In this paper, a bivariate copula-based regression model for temporary disability and permanent injury severities is introduced for the joint analysis of the relationship with the set of factors that might influence both categories of injury. Using a motor insurance database with 21,361 observations, the copula-based regression model is shown to give a better performance than that of a model based on the assumption of independence. The inclusion of the dependence structure in the analysis has a higher impact on the variance estimates of the injury severities than it does on the point estimates. By taking into account the dependence between temporary and permanent severities a more extensive factor analysis can be conducted. We illustrate that the conditional distribution functions of injury severities may be estimated, thus, providing decision makers with valuable information.

Some New Definitions of Indicators for the Choquet Integral

Aggregation operators are broadly used in decision making problems. These operators are often characterized by indicators. Numerous of these aggregation operators may be represented by means of the Choquet integral. In this article four different indicators usually associated to the ordered weighted averaging (OWA) operator are extended to the Choquet integral. In particular, we propose the extensions of the degree of balance, the divergence, the variance indicator and Renyi entropies. Indicators for the weighted ordered weighted averaging (WOWA) operator are derived to illustrate the application of results. Finally, an example is provided to show main contributions.

Influence of parties' behavioural features on motor compensation disputes in insurance markets

Disputes between parties involved in motor insurance claims compensations are analysed. The decision to resolve the disagreement by either negotiation or trial may depend on how risk and confrontation adverse or pessimistic the claimant is. The extent to which these behavioural features of the claimant might influence the final compensation amount is examined. An empirical analysis, fitting a switching regression model to a Spanish database, is conducted in order to analyse whether the choice of the conflict resolution procedure is endogenous to the compensation outcomes. The results show that compensations awarded by courts are always higher, although 95% of cases are settled by negotiation. We show that this is because claimants are adverse to risk and confrontation, and are pessimistic about their chances at trial. By contrast, insurers are risk/confrontation neutral and more objective in relation to the expected trial compensation. During the negotiation insurers accept to pay the subjective compensation values of claimants, since these values are lower than their estimates of compensations at trial.

Generalizing Some Usual Risk Measures in Financial and Insurance Applications

We illustrate a family of risk measures called GlueVaR that combine Value-at-Risk and Tail Value-at-Risk at different tolerance levels and have analytical closed-form expressions for the most frequently used distribution functions in financial and insurance applications, i.e. Normal, Log-normal, Student t and Generalized Pareto distributions. Tail-subadditivity is a remarkable property of a subfamily of GlueVaR risk measures. An implementation to the analysis of risk in an insurance portfolio is investigated.

Prevalence of drug use among drivers based on mandatory, random tests in a roadside survey

Background In the context of road safety, this study aims to examine the prevalence of drug use in a random sample of drivers. Methods A stratified probabilistic sample was designed to represent vehicles circulating on non-urban roads. Random drug tests were performed during autumn 2014 on 521 drivers in Catalonia (Spain). Participation was mandatory. The prevalence of drug driving for cannabis, methamphetamines, amphetamines, cocaine, opiates and benzodiazepines was assessed. Results The overall prevalence of drug use is 16.4% (95% CI: 13.9; 18.9) and affects primarily younger male drivers. Drug use is similarly prevalent during weekdays and on weekends, but increases with the number of occupants. The likelihood of being positive for methamphetamines is significantly higher for drivers of vans and lorries. Conclusions Different patterns of use are detected depending on the drug considered. Preventive drug tests should not only be conducted on weekends and at night-time, and need to be reinforced for drivers of commercial vehicles. Active educational campaigns should focus on the youngest age-group of male drivers.