An Analysis of Black-Box Optimization Problems in Reinsurance: Evolutionary-Based Approaches

Abstract

Black-box optimization problems (BBOP) are defined as those optimization problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program). This paper is focussed on BBOPs that arise in the field of insurance, and more specifically in reinsurance problems. In this area, the complexity of the models and assumptions considered to define the reinsurance rules and conditions produces hard black-box optimization problems, that must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in BBOP, so new computational paradigms must be applied to solve these problems. In this paper we show the performance of two evolutionary-based techniques (Evolutionary Programming and Particle Swarm Optimization). We provide an analysis in three BBOP in reinsurance, where the evolutionary-based approaches exhibit an excellent behaviour, finding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.