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5. Approximations for Life Annuities with Concept Comonotonicity

In insurance contexts, distribution function of sum of risks is interesting for individuals. Such a sum appears when considering aggregate claim of an insurance portfolio over a certain reference period. The assumption of mutual independence between the components of sum is not always acceptable and logical. Since the calculation of dependent risks are less tractable, and also because, in general, the statistics gathered by the insurer only give information about the marginal distribution of risks, therefore, it is only possible to get formula for the first couple of moments. To compute more complex risk measurements, like stop-loss premiums or upper quintiles, one has to rely on simulations; therefore, we will determine approximation for sum of risks, when the distributions of terms are known, but the stochastic dependence structure between them is unknown or too complex to work with. Like wise, we give an alternative solution for case of life annuities (and portfolio of life annuities) when also the stochastic nature rate is taken into account.