Estrategias óptimas de reaseguro proporcional para una cartera de pólizas de incendio

An insurance company may opt to transfer and distribute to a reinsurance company part of the risks assumed in its policy portfolio to mitigate losses that could generate financial inconveniences and weak its economic capacity. The relationship between the direct insurer and the reinsurer is carried out through a reinsurance contract, which specifies the obligations between both parties. In the present work, proportional reinsurance contracts of quota-share and surplus type are considered, in which the reinsurer assumes a certain proportion of the premiums and claims. Given a portfolio of national fire insurance policies, the main objective of this work is to determine the optimal level of risk retention that corresponds to the selected reinsurance contracts from the perspective of the mean-variance approach proposed by Bruno de Finetti (de Finetti, 1940). Under the assumption of independent risks, for each selected contract, the solution to the corresponding convex optimization problem is found. Given a selection of probability distributions for risk exposure and aggregate cost of claims, it is shown how to find in R (R Core Team, 2022) the optimal retention rates by risk class, also in the cases that require their truncation, as well as other characteristics of the portfolio under consideration that is relevant to compare the obtained results.