Aplicação do método de Benchmark no resseguro óptimo e avaliação de investimento em uma seguradora

Abstract

Insurance companies are important to society, as they guarantee financial protection to individuals against property losses, in addition to promoting the capital market through the allocation of guaranteeing assets. Therefore, it is essential to evaluate the instruments that guarantee its long-term financial solvency, such as reinsurance treaties. Reinsurance is the tool often used by insurance companies to reduce the level and volatility of aggregate claim burden under their responsibility. This work has the general objective of minimizing the robust value involving the expected time to reach a certain pre-established capital at a level before the ruin and penalty of the ambiguity model. Considering that the insurer does not have perfect information in terms of the risky asset drift and insurance risk, the study solved the optimal investment problem and robust reinsurance for the insurer under a surplus model considering that the insurer does not have perfect information in terms of the derivative of the risky asset and insurance risk. The insurer aims to mini- mize a robust value involving the probability of reaching a high target before ruin and a penalty for model ambiguity. To achieve this goal, the robust value function was cha- racterized as the only classical solution to the Hamilton–Jacobi–Bellman (HJB) equation. The value function was explicitly derived by solving the HJB equation and resulted in an optimal investment-reinsurance strategy and drift distortions of the optimal measure in benchmark forms. It was observed that the optimal strategy under the ambiguity penalty scenario coincides with the optimal strategy under minimizing the probability of reaching the objective in the unambiguous benchmark case. The impact of ambiguity aversion on insurer valuation and selection of optimal derivation distortions was also demonstrated. After applying the methodology and results obtained, it was possible to conclude that proportional reinsurance can be used and in some circumstances it may be cheap or not cheap so that insurance can be invested logically.