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La prima de riesgo recargada en un seguro de rentas: tarificación mediante el uso de una medida de riesgo coherente || The Risk Recharged Premium for a Survival Life Insurance: Recharged Premium through the Use of a Coherent Risk Measure

Author

Listed:
  • Hernández Solís, Montserrat

    (Departamento de Economía de la Empresa y Contabilidad, UNED)

  • Lozano Colomer, Cristina

    (Departamento de Métodos Cuantitativos, Universidad Pontificia de Comillas (ICADE))

  • Vilar Zanón, José Luis

    (Departamento de Economía Financiera y Actuarial, Universidad Complutense de Madrid)

Abstract

En este estudio se obtiene un principio de cálculo de primas, para el ramo de vida, basado en una medida de riesgo coherente, la esperanza distorsionada transformada proporcional del tanto instantáneo (Wang, 1995), que justifique la recomendación de Solvencia II de reducir, para un seguro de rentas, el efecto del tanto instantáneo de mortalidad y conseguir de este modo una prima recargada implícitamente para hacer frente a las desviaciones desfavorables de la siniestralidad real. La modalidad de seguro seleccionada para el estudio ha sido el de rentas, seguro con cobertura de supervivencia, calculándose la prima única de riesgo para las cuatro leyes de supervivencia más aceptadas, como son la primera y segunda de Dormoy, la ley de Gomperzt y la ley de Makeham. La selección de estas leyes ha sido por ser las que mejor se ajustan al modelo mediante el empleo de las tablas de mortalidad elaboradas por Pérez (2000). En los seguros de vida con cobertura de supervivencia, una experiencia de siniestralidad negativa para la compañía significa que los asegurados son más longevos de lo esperado. Así, cuando se calculan las primas, es una práctica común añadir un margen de seguridad implícito, en forma de porcentaje, a las probabilidades de fallecimiento qx, o bien emplear una tabla de mortalidad cuyas probabilidades de fallecimiento sean inferiores a las del grupo humano considerado. Esto se puede interpretar como un decremento del tanto instantáneo con un múltiplo. En este artículo se demuestra que el empleo de la función de distorsión, hasta ahora empleada en el ramo de no vida y siendo la novedad su aplicación al ramo de vida asegurador, produce este mismo efecto, pero mediante el cálculo de una prima recargada de manera implícita. || The goal of this study is to get a premium calculation principle, for the life insurance business, based on a coherent risk measure (Wang, 1995) in the form of power, called \Proportional Hazards (PH) Transforms" to justify the recommendation of Solvency II to reduce the effect of the mortality instantaneous rate and thus get an implicitly surcharged premium to deal deviations of actual claims regarding expected. Survival life insurance has been selected for this research, and the premium risk has been calculated for the four accepted laws of survival, such as the first and second Dormoy, Gomperzt law, and Makeham law. The selection of these laws has been taken because they best _t the model based on the numerical values assigned to the parameters by using mortality tables developed by Pérez (2000), Projected Table 2000 Spanish Mortality from 1950-1990. In the life insurance, coverage claims survival negative experience for the company means that the insured survive longer than expected (live longer). Thus, when calculating premiums, it is common practice to add a safety margin implied, as a percentage, the odds of death qx, or use a mortality table whose chances of passing are lower than those of the human being taken into account. This can be interpreted as a decrease of the mortality instantaneous rate. In this paper we show that the use of the distortion power function, so far uses in the non-life branch and being the new application to the life insurance, produces the same effect, but calculating a implicitly surcharged premium.

Suggested Citation

  • Hernández Solís, Montserrat & Lozano Colomer, Cristina & Vilar Zanón, José Luis, 2013. "La prima de riesgo recargada en un seguro de rentas: tarificación mediante el uso de una medida de riesgo coherente || The Risk Recharged Premium for a Survival Life Insurance: Recharged Premium throu," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 15(1), pages 151-167, June.
  • Handle: RePEc:pab:rmcpee:v:15:y:2013:i:1:p:151-167
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    References listed on IDEAS

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    More about this item

    Keywords

    seguro de rentas; recargo; medida de riesgo coherente; función de distorsión; survival life insurance (annuities); surcharge; coherent risk measure; distortion function;
    All these keywords.

    JEL classification:

    • M20 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics - - - General
    • C00 - Mathematical and Quantitative Methods - - General - - - General

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