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Prediction of individual automobile reported but not settled claim reserves for bodily injuries in the context of Solvency II = Predicción de las reservas individuales para siniestros del automóvil con daños corporales pendientes de liquidación en el contexto de Solvencia II

Listed author(s):
  • Ayuso Gutierrez, M. Mercedes


    (Departament d’Econometria, Estadística i Economia Espanyola, Universitat de Barcelona)

  • Santolino Prieto, Miguel Á.


    (Departament d’Econometria, Estadística i Economia Espanyola, Universitat de Barcelona)

Registered author(s):

    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 claims is therefore vital for insurers. In accordance with the recommendation included in the Solvency II project, a statistical model is implemented for reserve estimation. Lognormality on empirical 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 severity is predicted by means of a heteroscedastic multiple choice model, because evidence has found that the variability in the latent severity of individuals travelling by car is not constant. It is shown that this methodology improves the accuracy of reserve estimation at all stages, as compared to the subjective assessment that has traditionally been made by practitioners. = Los siniestros del automóvil con daños corporales suelen permanecer sin liquidar durante largos periodos después del accidente. Una adecuada estimación por siniestros comunicados pero no liquidados es por tanto de vital importancia para los aseguradores. Siguiendo las recomendaciones incluidas en el proyecto de Solvencia II, se implementa un método estadístico para la estimación de la reserva. En concreto, se observa que el coste de compensación se distribuye lognormalmente para diferentes niveles de gravedad del daño corporal. La provisión individual del siniestro la estimamos asignando el valor esperado de compensación media según la gravedad predicha de la lesión de la víctima, para la cual también se calcula el límite superior. La gravedad la predecimos mediante un modelo heterocedástico de elección múltiple, porque hallamos evidencias de que la variabilidad en la gravedad latente no es constante para los individuos que viajaban en un turismo. Se demuestra que la metodología propuesta mejora la precisión en la estimación de las reservas en todas las etapas, en comparación con la valoración subjetiva que ha sido tradicionalmente hecha por los peritos de la compañía.

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    Article provided by Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration in its journal Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration.

    Volume (Year): 6 (2008)
    Issue (Month): 1 (December)
    Pages: 23-41

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    Handle: RePEc:pab:rmcpee:v:6:y:2008:i:1:p:23-41
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    References listed on IDEAS
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    1. Larsen, Christian Roholte, 2007. "An Individual Claims Reserving Model," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(01), pages 113-132, May.
    2. England, P. D. & Verrall, R. J., 2006. "Predictive Distributions of Outstanding Liabilities in General Insurance," Annals of Actuarial Science, Cambridge University Press, vol. 1(02), pages 221-270, September.
    3. Ayuso, Mercedes & Santolino, Miguel, 2007. "Predicting automobile claims bodily injury severity with sequential ordered logit models," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 71-83, July.
    4. England, P.D. & Verrall, R.J., 2002. "Stochastic Claims Reserving in General Insurance," British Actuarial Journal, Cambridge University Press, vol. 8(03), pages 443-518, August.
    5. Norberg, Ragnar, 1993. "Prediction of Outstanding Liabilities in Non-Life Insurance," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 23(01), pages 95-115, May.
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