Reaseguro y reparto de dividendos como herramientas de control de la solvencia en una carteras de seguros no vida: Análisis desde la teoría colectiva del riesgo

The object of study of this paper is the analysis of the level of reserves in a non-life insurance portfolio. The approach to this tool as an indicator of the solvency of the portfolio poses an initial dilemma between the security necessary to be able to respond to the losses that have occurred and the problem generated financially by the fact of immobilizing reserves. We face therefore the disjunctive security-profitability. As a balancing element, the portfolio manager may consider the use of dividend distribution policies or reinsurance policies that are applied or modified at the time the reserves reach a certain level. Analyzing the problem from the classical hypotheses of the risk process, we consider in this work the probability that the reserves reach that predetermined level, at which time the manager may rethink his policies. This probability is obtained for a general case in which the inter-accident times and the individual amount of the loss are modeled with Erlang distributions. Finally, we present examples and numerical results that can help to understand the behavior of this probability.