Comparison of Multi-Objective Evolutionary Algorithms in Optimizing Combinations of Reinsurance Contracts ABSTRACT

In many branches of the insurance business the insurance company is not willing (or not able) to hold the entire risk on its own. There are several types of treaties which an insurance company can use to cede an amount of its claims to another insurance company. A substantial amount of research has been performed to find individually optimal structures for each of these types of reinsurance treaties. However only few results exist when the goal is to find optimal combinations of reinsurance treaties because of computational complexity or non-convexity of the objective functions. In our paper we introduce a novel approach to solve this task. For the first time this problem will be treated like a true multiobjective optimization problem. We apply two state-of-theart MOEAs, the NSGA-II and the ɛ-MOEA and compare their results in our problem setting. The presented approach is flexible with respect to real world modifications concerning risk measurement, cost calculation principles and different combinations of reinsurance treaties. Finally, we do not only solve open mathematical problems on complex reinsurance combinations but we consequently give new heuristic interpretations to supplement existing theoretic results