Modelización Estocástica de Probabilidad de Ruina para empresas de seguro en la rama de vehículos en Ecuador

The Insurance Law in Ecuador imposes several conditions to protect insurers in order to allow them to fulfill all their obligations. These conditions are, for example, a minimum value of the reserves (USD 8,0,000.00), as well as the possibility of carrying out investment activities in order to cover different kinds of risks. However, due to the dynamism of this activity, the conditions established by the Law are not sufficient to avoid the ruin of an insurance company. In such, it is important to find new mechanisms to protect these companies. This work develops a stochastic model under the Monte Carlo Simulation, which calculates the probability of ruin for a chosen car insurer company, denominated ABC. This is a collective model of non-life under the scoops from the model of the authors D. Daykinet al., since it is adjusted to the financial and economic variables of an insurance company. Under the parameters of the ABC company, including an initial reserve around USD. 8,0,000.00 as indicatedby the Law; a 73% probability is obtained which is quite high and troublesome. With this result it is not possible to continue with the activity. As a solution, the model is simulated again with the same parameters except for the initial reserve, increasing it to USD. 9,0,000.00, which result in a ruin probability of 0%. With these results it can be concluded that the minimum reserve value established by the Insurance Law is not sufficient to guarantee solvency and to cover risks. In this regard, the proposed stochastic modeling helps to prevent the insolvency of an insurance company.