Application of a coherent risk measure in the price calculation of an income insurance (annuities)

  1. Hernández Solís, Montserrat
  2. Berenguer Cárceles, Emma
Pecunia: revista de la Facultad de Ciencias Económicas y Empresariales

ISSN: 1699-9495

Year of publication: 2013

Issue: 16-17

Pages: 41-54

Type: Article

DOI: 10.18002/PEC.V0I16/17.1334 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

More publications in: Pecunia: revista de la Facultad de Ciencias Económicas y Empresariales


Modification of instantaneous mortality rates when applying the net premium principle in order to cope with unfavorable deviations in claims, is common practice carried out by insurance companies. This paper provides a mathematical answer to this matter by applying Wang's power distortion function. Both net premium and Wang's distortion function are coherent risk measures, the latter being first applied to the field of life insurance. Using the Gompertz and Makeham laws we first calculate the premium at a general level and in a second part, the principle of premium calculation based on Wang´s power distortion function is applied to calculate the adjusted risk premium surcharge. The risk single premium pricing has been applied to a form of survival insurance coverage called Annuities. The main conclusion to be drawn is that by using the distortion function, the new instantaneous mortality rate is directly proportional to a multiple, which happens to be the exponent of this function and causes longevity risk to be greater. This is why the adjusted risk premium is higher than the net premium

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