Prediction of individual automobile RBNS claim reserves in the context of Solvency II

Automobile bodily injury (BI) claims remain unsettled for a long time after the accident. The estimation of an accurate reserve for Reported But Not Settled (RBNS) claims is therefore vital for insurers. In accordance with the recommendation included in the Solvency II project (CEIOPS, 2007) a statistical model is here implemented for RBNS reserve estimation. Lognormality on empirical compensation cost data is observed for different levels of BI severity. The individual claim provision is estimated by allocating the expected mean compensation for the predicted severity of the victim’s injury, for which the upper bound is also computed. The BI severity is predicted by means of a heteroscedastic multiple choice model, because empirical evidence has found that the variability in the latent severity of injured individuals travelling by car is not constant. It is shown that this methodology can improve the accuracy of RBNS reserve estimation at all stages, as compared to the subjective assessment that has traditionally been made by practitioners.Automobile accident, Solvency II, bodily injury claims, individual RBNS reserve..

Forecasting the maximum compensation offer in the automobile BI claims negotiation proces.

Most motor bodily injury (BI) claims are settled by negotiation, with fewer than 5% of cases going to court. A well-defined negotiation strategy is thus very useful for insurance companies. In this paper we assume that the monetary compensation awarded in court is the upper amount to be offered by the insurer in the negotiation process. Using a real database, a log-linear model is implemented to estimate the maximal offer. Non-spherical disturbances are detected. Correlation occurs when various claims are settled in the same judicial verdict. Groupwise heteroscedasticity is due to the influence of the forensic valuation on the final compensation amount. An alternative approximation based on generalized inference theory is applied to estimate confidence intervals on variance components, since classical interval estimates may be unreliable for datasets with unbalanced structures.bodily injury claims compensation, negotiation process, generalized confidence intervals.

Selection bias and auditing policies for insurance claims

Les biais de sélection sont créés par des disparités entre le domaine d'estimation d'un modèle statistique et son domaine d'application. C'est le cas pour les modèles évaluant le risque de fraude, qui sont estimés sur les seuls sinistres audités mais appliqués sur tous les sinistres entrants. Or les sinistres audités sont une minorité, étant choisis suite à une sélection sévère effectuée par des experts. Ce papier présente une approche statistique qui contrebalance le biais de sélection sans recourir à une stratégie d'audit aléatoire. On estime un modéle à deux équations sur l'audit et la fraude (un modèle probit bivarié avec censure), sur une une partie d'une base de sinistres où les experts sont laissés libres de leur décision d'auditer. On corrige ainsi la surestimation attendue du risque de fraude en cas d'estimation d'une seule équation. Les résultats sont proches de ceux obtenus par audit aléatoire, au prix d'une instabilité des résultats par rapport à l'ensemble des composantes de régression. On compare ensuite des politiques d'audit à partir des différentes approches.

La mediació dins la piràmide de litigiositat per a Catalunya : anàlisi de costos

Amb el disseny d'una piràmide de litigiositat es pretén quantificar el nombre de casos observats en cadascuna de les etapes per les quals pot passar la resolució d'un conflicte, des que es genera, fins que es resol. La mediació intenta arribar a l'acord entre les parts enfrontades mitjançant la intervenció d'una tercera persona, i se situa en els nivells superiors de la piràmide, a la mateixa altura que altres formes alternatives de resolució de conflictes (com la negociació o l'arbitratge), i just abans de la resolució en els tribunals de justícia. El desenvolupament de la mediació com a sistema abasta-ment acceptat en la resolució de conflictes en una zona geogràfica, o davant diferents tipologies de casos, passa per realitzar una anàlisi exhaustiva sobre la seva eficiència, tenint en compte els costos de la seva implementació, i l'estalvi generat. Per a realitzar aquest procés en sistemes en els quals el desenvolupament de la mediació no és exhaustiu, i s'ha vist limitat a la resolució de determinats tipus de conflictes, resulta necessari aprofundir, en primer lloc, en les anàlisis de la capa superior de la piràmide de litigiositat, amb l'estudi dels indicadors habitualment utilitzats en el mesurament de la justícia ordinària. A continuació passarem a analitzar l'impacte que en aquests indicadors tindria el desenvolupament de metodologies alternatives de resolució de conflictes. Els resultats tenen en compte el marc de la recent entrada en vigor de la Llei 15/2009 de 22 de juliol, de Mediació en l'àmbit del Dret Privat de Catalunya

Prediction of individual automobile RBNS claim reserves in the context of Solvency II

Automobile bodily injury (BI) claims remain unsettled for a long time after the accident. The estimation of an accurate reserve for Reported But Not Settled (RBNS) claims is therefore vital for insurers. In accordance with the recommendation included in the Solvency II project (CEIOPS, 2007) a statistical model is here implemented for RBNS reserve estimation. Lognormality on empirical compensation cost data is observed for different levels of BI severity. The individual claim provision is estimated by allocating the expected mean compensation for the predicted severity of the victim’s injury, for which the upper bound is also computed. The BI severity is predicted by means of a heteroscedastic multiple choice model, because empirical evidence has found that the variability in the latent severity of injured individuals travelling by car is not constant. It is shown that this methodology can improve the accuracy of RBNS reserve estimation at all stages, as compared to the subjective assessment that has traditionally been made by practitioners

Forecasting the maximum compensation offer in the automobile BI claims negotiation process

Most motor bodily injury (BI) claims are settled by negotiation, with fewer than 5% of cases going to court. A well-defined negotiation strategy is thus very useful for insurance companies. In this paper we assume that the monetary compensation awarded in court is the upper amount to be offered by the insurer in the negotiation process. Using a real database, a log-linear model is implemented to estimate the maximal offer. Non-spherical disturbances are detected. Correlation occurs when various claims are settled in the same judicial verdict. Group wise heteroscedasticity is due to the influence of the forensic valuation on the final compensation amount. An alternative approximation based on generalized inference theory is applied to estimate confidence intervals on variance components, since classical interval estimates may be unreliable for datasets with unbalanced structures

Number and severity of BI victims, assuming dependence between vehicles involved in the crash

The number of victims in vehicles in Spanish motor crashes is analyzed by bodily injury (BI) severity level. Generalized linear mixed models (GLMMs) are applied to model the number of non-serious victims, serious victims and fatalities. Dependence between vehicles involved in the same crash is captured including random effects. After comparing between error distributions, the binomial GLMM is selected. The effect of the driver, vehicle and crash characteristics on the number of BI victims by severity level is analyzed, paying special attention to the influence of the age of the driver and the age of the vehicle. We found a nonlinear relationship between driver’s age and severity, with young and older drivers being the riskiest groups. On the other hand, the expected severity of the crash linearly increased with the vehicle age until the vehicle was 18 years old and then remained constant at the highest severity level from that age. These results are relevant in countries such as Spain with increasing longevity of drivers and aging of the car fleet

Desarrollo metodológico del modelo actuarial de múltiples estados casado – viudo y cálculo actuarial del coste por pensiones de jubilación y viudedad

El objetivo de este trabajo es desarrollar metodológicamente un modelo actuarial de múltiples estados que permita probabilizar la transición entre los estados civiles casado-viudo para individuos de una determinada edad x. Dichas probabilidades se utilizarán en el cálculo del valor esperado de los pagos por concurrencia de pensiones para individuos de 65 o más años

Modelo actuarial multiestado para el cálculo de probabilidades de supervivencia y fallecimiento según estado civil: una aplicación al pago de pensiones concurrentes

El estudio del efecto que factores endógenos como el estado civil de la persona tienen en el comportamiento de indicadores biométricos, económicos y sociales relacionados con el sistema de bienestar de un país es un tema de máxima relevancia en la actualidad. En España, la creciente longevidad y el mayor número de mujeres generadoras de pensión de jubilación ha puesto en entredicho el actual sistema de pensiones contributivas de viudedad, para el que se espera un notable incremento de prestaciones. El desarrollo metodológico de un modelo actuarial de múltiples estados según el estado civil de la persona cobra por tanto máximo interés

Linking pensions to life expectancy: tackling conceptual uncertainty through Bayesian Model Averaging

Linking pensions to longevity developments at retirement age has been one of the most common policy responses of pension schemes to aging populations. The introduction of automatic stabilizers is primarily motivated by cost containment objectives, but there are other dimensions of welfare restructuring in the politics of pension reforms, including recalibration, rationalization, and blame avoidance for unpopular policies that involve retrenchments. This paper examines the policy designs and implications of linking entry pensions to life expectancy developments through sustainability factors or life expectancy coefficients in Finland, Portugal, and Spain. To address conceptual and specification uncertainty in policymaking, we propose and apply a Bayesian model averaging approach to stochastic mortality modeling and life expectancy computation. The results show that: (i) sustainability factors will generate substantial pension entitlement reductions in the three countries analyzed; (ii) the magnitude of the pension losses depends on the factor design; (iii) to offset pension cuts and safeguard pension adequacy, individuals will have to prolong their working lives significantly; (iv) factor designs considering cohort longevity markers would have generated higher pension cuts in countries with increasing life expectancy gap