Cálculo de la rentabilidad esperada y cuantificación del riesgo en una operación de ahorro de capital diferido a prima (pura y comercial) única

This paper develops a financial-actuarial methodology to determine the financial-fiscal profitability an insured can obtain by contracting a deferred capital transaction. Since this transaction is conditioned on the insured's survival probability, it has a random return dependent on the probability distribution associated to the aforementioned survival. We define the expected return and, on the basis of the probability distribution of the current value of the product's benefit random variable, we obtain decision parameters that reflect the risk of the operation as well as its influence on the expected return. Our theoretical development will be carried out for single premiums under the assumption of pure premium and overcharged premium, and taking into consideration taxes and tax deductions. Finally, we propose an empirical analysis of the cases under our focus of attention, which will show the applicability of the results thus obtained, all for the purpose of providing the insured with the maximum information to make his or her decision within a random environment.