Tarificación de un seguro de invalidez: una aplicación al caso ecuatoriano.

Abstract

In this work we present the basic notions of actuarial mathematics, linear algebra and stochastic processes; in addition to a brief summary of the Runge Kutta numerical method of order 4. Subsequently, considering the Ecuadorian social security regulations, we will propose a disability insurance congruent with the current x x economic and demographic conditions of Ecuador. We will see this insurance as a three-state Markov chain, so we will propose a system of ordinary differential equations using the Kolmogorov differential equation. We will solve this system analytically through the use of linear algebra, and numerically through the application of the Runge Kutta method of order 4. Once the system is solved, we will have the transition probabilities of the insured; necessary to quantify the premium of the formulated product, as a term immediate annuity. Finally, we compare the obtained solutions with both methods