An evolutionary strategy for multiobjective reinsurance optimization

Abstract

In this work we tackle a multiobjective reinsurance optimization problem (MOROP) from the point of view of an insurance company. The MOROP seeks to find a reinsurance program that optimizes two conflicting objectives: the maximization of the expected value of the profit of the company and the minimization of the risk of the insurance losses retained by the company. To calculate these two objectives we built a probabilistic model of the portfolio of risks of the company. This model is embedded within an evolutionary strategy (ES) that approximates the efficient frontier of the MOROP using a combination of four classical reinsurance structures: surplus, quota share, excess-of-loss and stop-loss. Computational experiments with the risks of a specific line of business of a large Colombian general insurance company show that the proposed evolutionary strategy outperforms the classical non-dominated sorting genetic algorithm. Moreover, the analysis of the solutions in the efficient frontier obtained with our ES gave several insights to the company in terms of the structure and properties of the solutions for different risk-return trade-offs.