La prima de riesgo recargada en un seguro de rentas : tarificación mediante el uso de una medida de riesgo coherente

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.