Formulación de un plan de seguros de vida para familias mediante modelos de dependencia: una aplicación al caso ecuatoriano.

Abstract

In this curricular integration work, a multiple life insurance policy was developed using the theory of dependency models, starting by defining the last survivor extinction status, in which a group ceases to exist only if all its members have died. Afterwards, the expressions for the probabilities for the last survivor status and general transition using properties of Markov chains and Probability theory. Subsequently, we introduced the positive quadrant dependence property which allows us to establish that the remaining lives of the members of a family depend on the life status of the other members of the family. Then, we calculated the expressions of the premium and annuity of the last survivor life insurance as a function of the transition probabilities and properties of Markov chains. We estimated the Gompertz and Makeham mortality law parameters and estimates of mortality forces derived from positive quadrant dependence. Finally, all the above was implemented using libraries of the statistical software R, the pure premium was calculated, and internal and external management surcharges were applied, any other additional surcharge will be very easy to implement; the results obtained have been compared with individual life insurance with respect to its reserve and premiums, and it was determined that the life insurance developed is the best option to insure the members of an Ecuadorian family.